[ABDF11] M. V., Afonso, J. M., Bioucas-Dias, and M. A. T., Figueiredo, An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,IEEE Transactions on Image Processing 20 (2011), no. 3, 681-695.Google Scholar

[ABT01] A., Achim, A., Bezerianos, and P., Tsakalides, Novel Bayesian multiscale method for speckle removal in medical ultrasound images,IEEE Transactions on Medical Imaging 20 (2001), no. 8, 772-783.Google Scholar

[AG01] A., Aldroubi and K., Gröchenig, Nonuniform sampling and reconstruction in shift-invariant spaces,SIAM Review 43 (2001), 585-620.Google Scholar

[Ahm74] N., Ahmed, Discrete cosine transform,IEEE Transactions on Communications 23 (1974), no. 1, 90-93.Google Scholar

[AKBU13] A., Amini, U. S., Kamilov, E., Bostan, and M., Unser, Bayesian estimation for continuous-time sparse stochastic processes,IEEE Transactions on Signal Processing 61 (2013), no. 4, 907-920.Google Scholar

[Ald95] A., Aldroubi, Portraits of frames,Proceedings of the American Mathematical Society 123 (1995), no.61661-1668.Google Scholar

[App09] D., Appelbaum, Lévy Processes and Stochastic Calculus, 2nd edn., Cambridge University Press, 2009.Google Scholar

[AS72] M., Abramowitz and I. A., Stegun, Handbook of Mathematical Functions,National Bureau of Standards, 1972.Google Scholar

[AS83] D. A., Agard and J. W., Sedat, Three-dimensional architecture of a polytene nucleus,Nature 302 (1983), no. 5910, 676-681.Google Scholar

[ASS98] F., Abramovich, T., Sapatinas, and B. W., Silverman, Wavelet thresholding via a Bayesian approach,Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60 (1998), no. 4, 725-749.Google Scholar

[ATB03] A., Achim, P., Tsakalides, and A., Bezerianos, SAR image denoismg via Bayesian wavelet shrinkage based on heavy-tailed modeling,IEEE Transactions on Geoscience and Remote Sensing 41 (2003), no. 8, 1773-1784.Google Scholar

[AU94] A., Aldroubi and M., Unser, Sampling procedures in function spaces and asymptotic equivalence with Shannon's sampling theory,Numerical Functional Analysis and Optimization 15 (1994), no. 1-2, 1-21.Google Scholar

[AU14] A., Amini and M., Unser, Sparsity and infinite divisibility,IEEE Transactions on Information Theory 60 (2014), no. 4, 2346-2358.Google Scholar

[AUM11] A., Amini, M., Unser, and F., Marvasti, Compressibility of deterministic and random infinite sequences,IEEE Transactions on Signal Processing 59 (2011), no. 11, 5193-5201.Google Scholar

[Bar61] M. S., Bartlett, An Introduction to Stochastic Processes, with Special Reference to Methods and Applications,Cambridge Universty Press, 1961.Google Scholar

[BAS07] M. I. H., Bhuiyan, M. O., Ahmad, and M. N. S., Swamy, Spatially adaptive wavelet-based method using the Cauchy prior for denoising the SAR images,IEEE Transactions on Circuits and Systems for Video Technology 17 (2007), no. 4, 500-507.Google Scholar

[BDE09] A. M., Bruckstein, D. L., Donoho, and M., Elad, From sparse solutions of systems of equations to sparse modeling of signals and images,SIAMReview 51 (2009), no. 1, 34-81.Google Scholar

[BDF07] J. M., Bioucas-Dias and M. A. T., Figueiredo, A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,IEEE Transactions on Image Processing 16 (2007), no. 12, 2992-3004.Google Scholar

[BDR02] A., Bose, A., Dasgupta, and H., Rubin, A contemporary review and bibliography of infinitely divisible distributions and processes,Sankhya: The Indian Journal of Statistics: Series A 64 (2002), no. 3, 763-819.Google Scholar

[Ber52] H., Bergström, On some expansions of stable distributions,Arkiv für Mathematik 2 (1952), no. 18, 375-378.Google Scholar

[BF06] L., Boubchir and J. M., Fadili, A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior,Pattern Recognition Letters 27 (2006), no. 12, 1370-1382.Google Scholar

[BH10] P. J., Brockwell and J., Hannig, CARMA(p,q) generalized random processes,Journal of Statistical Planningand Inference 140 (2010), no. 12, 3613-3618.Google Scholar

[BK51] M. S., Bartlett and D. G., Kendall, On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology,Mathematical Proceedings of the Cambridge Philosophical Society 47 (1951), 65-76.Google Scholar

[BKNU13] E., Bostan, U. S., Kamilov, M., Nilchian, and M., Unser, Sparse stochastic processes and discretization of linear inverse problems,IEEE Transactions on Image Processing 22 (2013), no. 7, 2699-2710.Google Scholar

[BM02] P., Brémaud and L., Massoulié, Power spectra of general shot noises and Hawkes point processes with a random excitation,Advances in Applied Probability 34 (2002), no. 1, 205-222.Google Scholar

[BNS01] O. E., Barndorff-Nielsen and N., Shephard, Non-Gaussian Ornstein-Uhlenbeckbased models and some of their uses in financial economics,Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2001), no. 2, 167-241.Google Scholar

[Boc32] S., Bochner, Vorlesungen über Fouriersche Integrale,Akademische Verlagsgesellschaft, 1932.Google Scholar

[Boc47] Stochastic processes, Annals of Mathematics 48 (1947), no. 4, 1014-1061.

[Bog07] V. I., Bogachev, Measure Theory, Vol. I, II, Springer, 2007.Google Scholar

[BPCE10] S., Boyd, N., Parikh, E., Chu, and J., Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers,Information Systems Journal 3 (2010), no. 1, 1-122.Google Scholar

[Bro01] P. J., Brockwell, Lévy-driven CARMA processes,Annals of the Institute of Statistical Mathematics 53 (2001), 113-124.Google Scholar

[BS50] H. W., Bode and C. E., Shannon, A simplified derivation of linear least square smoothing and prediction theory,Proceedings of the IRE 38 (1950), no. 4, 417-425.Google Scholar

[BS93] C., Bouman and K., Sauer, A generalized Gaussian image model for edgepreserving MAP estimation,IEEE Transactions on Image Processing 2 (1993), no. 3, 296-310.Google Scholar

[BT09a] A., Beck and M., Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,IEEE Transactions on Image Processing 18 (2009), no. 11, 2419-2434.Google Scholar

[BT09b] Afast iterative shrinkage-thresholding algorithm forlinearinverse problems,SIAM Journal on Imaging Sciences 2 (2009), no. 1, 183-202.

[BTU01] T., Blu, P., Thévenaz, and M., Unser, MOMS: Maximal-order interpolation of minimal support,IEEE Transactions on Image Processing 10 (2001), no. 7, 1069-1080.Google Scholar

[BU03] T., Blu and M., Unser, A complete family of scaling functions: The (a,α τ fractional splines, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'03) (Hong Kong SAR, People's Republic of China, April 6-10, 2003), vol. VI, IEEE, pp. 421-424.

[BU07] Self-similarity. Part II: Optimal estimation of fractal processes,IEEE Transactions on Signal Processing 55 (2007), no. 4, 1364-1378.

[BUF07] K. T., Block, M., Uecker, and J., Frahm, Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint,Magnetic Resonance in Medicine 57 (2007), no. 6, 1086-1098.Google Scholar

[BY02] B., Bru and M., Yor, Comments on the life and mathematical legacy of Wolfgang Döblin,Finance and Stochastics 6 (2002), no. 1, 3-47.Google Scholar

[Car99] J. F., Cardoso and D. L., Donoho, Some experiments on independent component analysis of non-Gaussianprocesses, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics (SPW-HOS'99) (Caesarea, Istael, June 14-16, 1999), 1999, pp. 74-77.Google Scholar

[CBFAB97] P., Charbonnier, L., Blanc-Féraud, G., Aubert, and M., Barlaud, Deterministic edge-preserving regularization in computed imaging,IEEE Transactions on Image Processing 6 (1997), no. 2, 298-311.Google Scholar

[CD95] R. R., Coifman and D. L., Donoho, Translation-invariant de-noising, Wavelets and statistics, (A., Antoniadis and G, Oppeheim, eds.), Lecture Notes in Statistics, vol. 103, Springer, 1995, pp. 125-150.Google Scholar

[CDLL98] A., Chambolle, R. A., DeVore, N.-Y., Lee, and B. J., Lucier, Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage,IEEE Transactions on Image Processing 7 (1998), no. 33, 319-335.Google Scholar

[Chr03] O., Christensen, An Introduction to Frames and Riesz Bases,Birkhäuser, 2003.Google Scholar

[CKM97] H. A., Chipman, E. D., Kolaczyk, and R. E., McCulloch, Adaptive Bayesian wavelet shrinkage,Journal of the American Statistical Association 92 (1997), no. 440, 1413-1421.Google Scholar

[CLM+95] W. A., Carrington, R. M., Lynch, E. D., Moore, G., Isenberg, K. E., Fogarty, and F. S., Fay, Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,Science 268 (1995), no. 5216, 1483-1487.Google Scholar

[CNB98] M. S., Crouse, R. D., Nowak, and R. G., Baraniuk, Wavelet-based statistical signal processing using hidden Markov models,IEEE Transactions on Signal Processing 46 (1998), no. 4, 886-902.Google Scholar

[Com94] P., Comon, Independent component analysis: A new concept,Signal Processing 36 (1994), no. 3, 287-314.Google Scholar

[CP11] P. L., Combettes and J.-C., Pesquet, Proximal splitting methods insignal processing, Fixed-Point Algorithms for Inverse Problems in Science and Engineering (H. H., Bauschke, R. S., Burachik, P. L., Combettes, V., Elser, D. R., Luke, and H., Wolkowicz, eds.), vol. 49, SpringerNew York, 2011, pp. 185-212.Google Scholar

[Cra40] H., Cramér, On the theory of stationary random processes,The Annals of Mathematics 41 (1940), no. 1, 215-230.Google Scholar

[CSE00] C., Christopoulos, A. S., Skodras, and T., Ebrahimi, The JPEG2000 still image coding system: An overview,IEEE Transactions on Consumer Electronics 16 (2000), no. 4, 1103-1127.Google Scholar

[CT04] R., Cont and P., Tankov, Financial Modelling with Jump Processes,Chapman & Hall, 2004.Google Scholar

[CU10] K. N., Chaudhury and M., Unser, On the shiftability of dual-tree complex wavelet transforms,IEEE Transactions on Signal Processing 58 (2010), no. 1, 221-232.Google Scholar

[CW91] C. K., Chui and J.-Z., Wang, A cardinal spline approach to wavelets,Proceedings of the American Mathematical Society 113 (1991), no. 3, 785-793.Google Scholar

[CW08] E. J., Candès and M. B., Wakin, An introduction to compressive sampling,IEEE Signal Processing Magazine 25 (2008), no. 2, 21-30.Google Scholar

[CYV00] S. G., Chang, B., Yu, and M., Vetterli, Spatially adaptive wavelet thresholding with context modeling for image denoising,IEEE Transactions on Image Processing 9 (2000), no. 9,1522 -1531.Google Scholar

[Dau88] I., Daubechies, Orthogonal bases of compactly supported wavelets,Communications on Pure and Applied Mathematics 41 (1988), 909-996.Google Scholar

[Dau92] Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, 1992.

[dB78] C., de Boor, A Practical Guide to Splines,Springer, 1978.Google Scholar

[dB87] The polynomials in the linear span of integer translates of a compactly supported function,Constructive Approximation 3 (1987), 199-208.

[dBDR93] C., de Boor, R. A., DeVore, and A., Ron, On the construction of multivariate (pre) wavelets,Constructive Approximation 9 (1993), 123-123.Google Scholar

[DBFZ+06] N., Dey, L., Blanc-Féraud, C., Zimmer, P., Roux, Z., Kam, J.-C., Olivo-Marin, and J., Zerubia, Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,Microscopy Research and Technique 69 (2006), no. 4, 260-266.Google Scholar

[dBH82] C., de Boor and K., Höllig, B-splines from parallelepipeds,Journal d'Analyse Mathématique 42 (1982), no. 1, 99-115.Google Scholar

[dBHR93] C., de Boor, K., Höllig, and S., Riemenschneider, Box Splines,Springer, 1993.Google Scholar

[DDDM04] I., Daubechies, M., Defrise, and C., De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,Communications on Pure and Applied Mathematics 57 (2004), no. 11, 1413-1457.Google Scholar

[DJ94] D. L., Donoho and I. M., Johnstone, Ideal spatial adaptation via wavelet shrinkage,Biometrika 81 (1994), 425-455. rican Statistical Association 90 (1995), no. 432, 1200-1224.Google Scholar

[Don95] D. L., Donoho, De-noising by soft-thresholding,IEEE Transactions on Information Theory 41 (1995), no. 3, 613-627.Google Scholar

[Don06] Compressed sensing,IEEE Transactions on Information Theory 52 (2006), no. 4, 1289-1306.

[Doo37] J. L., Doob, Stochastic processes depending on a continuous parameter,Transactions of the American Mathematical Society 42 (1937), no. 1, 107-140.Google Scholar

[Doo90] Stochastic Processes,John Wiley & Sons, 1990.

[Duc77] J., Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces, Constructive Theory of Functions of Several Variables (W., Schempp and K., Zeller, eds.), Springer, 1977, pp. 85-100.Google Scholar

[Ehr54] L., Ehrenpreis, Solutions of some problems of division I,American Jourmal of Mathematics 76 (1954), 883-903.Google Scholar

[EK00] R., Estrada and R. P., Kanwal, Singular Integral Equations,Birkhäuser, 2000.Google Scholar

[ENU12] A., Entezari, M., Nilchian, and M., Unser, A box spline calculus for the discretization of computed tomography reconstruction problems,IEEE Transactions on Medical Imaging 31 (2012), no. 8, 1532-1541.Google Scholar

[Fag14] J., Fageot, A., Amini and M., Unser, On the continuity of characteristic functionals and sparse stochastic modeling, Preprint (2014), arXiv:1401.6850(math.PR).Google Scholar

[FB05] J. M., Fadili and L., Boubchir, Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities,IEEE Transactions on Image Processing 14 (2005), no. 2, 231-240.Google Scholar

[FBD10] M. A. T., Figueiredo and J., Bioucas-Dias, Restoration of Poissonian images using alternating direction optimization,IEEE Transactions on Image Processing 19 (2010), no. 12, 3133-3145.Google Scholar

[Fel71] W., Feller, An Introduction to Probability Theory and its Applications, vol. 2, John Wiley & Sons, 1971.Google Scholar

[Fer67] X., Fernique, Lois indéfiniment divisibles sur l'espace des distributions,Inventiones Mathematicae 3 (1967), no. 4, 282-292.Google Scholar

[Fie87] D. J., Field, Relations between the statistics of natural images and the response properties of cortical cells,Journal of the Optical Society of America A: Optics Image Science and Vision 4 (1987), no. 12, 2379-2394.Google Scholar

[Fla89] P., Flandrin, On the spectrum of fractional Brownian motions,IEEE Transactions on Information Theory 35 (1989), no. 1, 197-199.Google Scholar

[Fla92] Wavelet analysis and synthesis of fractional Brownian motion,IEEE Transactions on Information Theory 38 (1992), no. 2, 910-917.

[FN03] M. A. T., Figueiredo and R. D., Nowak, An EM algorithm for wavelet-based image restoration,IEEE Transactions on Image Processing 12 (2003), no. 8, 906-916.Google Scholar

[Fou77] J., Fournier, Sharpness in Young's inequality for convolution,Pacific Journal of Mathematics 72 (1977), no. 2, 383-397.Google Scholar

[FR08] M., Fornasier and H., Rauhut, Iterative thresholding algorithms,Applied and Computational Harmonic Analysis 25 (2008), no. 2, 187-208.Google Scholar

[Fra92] J., Frank, Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope,Springer, 1992.Google Scholar

[Fre00] D. H., Fremlin, Measure Theory, Vol. 1, Torres Fremlin, 2000.Google Scholar

[Fre01] Measure Theory, Vol. 2,Torres Fremlin, 2001.

[Fre02] Measure Theory, Vol. 3,Torres Fremlin, 2002.

[Fre03] Measure Theory, Vol. 4,Torres Fremlin, 2003.

[Fre08] Measure Theory, Vol. 5,Torres Fremlin, 2008.

[GBH70] R., Gordon, R., Bender, and G. T., Herman, Algebraic reconstruction techniques (ART) forthree-dimensional electron microscopy and X-rayphotography,Journal of Theoretical Biology 29 (1970), no. 3, 471-481.Google Scholar

[Gel55] I. M., Gelfand, Generalized random processes,Doklady Akademii Nauk SSSR 100 (1955), no. 5, 853-856, in Russian.Google Scholar

[GG84] S., Geman and D., Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,IEEE Transactions on Pattern Analysis and Machine Intelligence 6 (1984), no. 6, 721-741.Google Scholar

[GK68] B. V., Gnedenko and A. N., Kolmogorov, Limit Distributions for Sums of Independent Random Variables,Addison-Wesley, 1968.Google Scholar

[GKHPU11] M., Guerquin-Kern, M., Häberlin, K. P., Pruessmann, and M., Unser, A fast wavelet-based reconstruction method for magnetic resonance imaging,IEEE Transactions on Medical Imaging 30 (2011), no. 9, 1649-1660.Google Scholar

[GR92] D., Geman and G., Reynolds, Constrained restoration and the recovery of discontinuities,IEEE Transactions on Pattern Analysis and Machine Intelligence 14 (1992), no. 3, 367-383.Google Scholar

[Gra08] L., Grafakos, Classical Fourier Analysis,Springer, 2008.Google Scholar

[Gri11] R., Gribonval, Should penalized least squares regression be interpreted as maximum a posteriori estimation?,IEEE Transactions on Signal Processing 59 (2011), no. 5, 2405-2410.Google Scholar

[Gro55] A., Grothendieck, Produits tensoriels topologiques et espaces nucléaires,Memoirs of the American Mathematical Society 16 (1955).Google Scholar

[GS64] I. M., Gelfand and G., Shilov, Generalized Functions, Vol. 1: Properties and Operations,Academic Press, 1964.Google Scholar

[GS68] Generalized Functions, Vol. 2: Spaces of Fundamental and Generalized Functions,Academic Press, New York, 1968.

[GS01] U., Grenander and A., Srivastava, Probability models for clutter in natural images,IEEE Transactions on Pattern Analysis and Machine Intelligence 23 (2001), no. 4, 424-429.Google Scholar

[GV64] I. M., Gelfand and N. Ya., Vilenkin, Generalized Functions, Vol. 4: Applications of Harmonic Analysis,Academic Press, New York, 1964.Google Scholar

[Haa10] A., Haar, Zur Theorie der orthogonalen Funktionensysteme,Mathematische Annalen 69 (1910), no. 3, 331-371.Google Scholar

[Hea71] O., Heaviside, Electromagnetic Theory: Including an Account of Heaviside's Unpublished Notes for a Fourth Volume,Chelsea Publishing, 1971.Google Scholar

[HHLL79] G. T., Herman, H., Hurwitz, A., Lent, and H. P., Lung, On the Bayesian approach to image reconstruction,Information and Control 42 (1979), no. 1, 60-71.Google Scholar

[HKPS93] T., Hida, H.-H., Kuo, J., Potthoff, and L., Streit, White Noise: An Infinite Dimensional Calculus,Kluver, 1993.Google Scholar

[HK70] A. E., Hoerl and R. W., Kennard, Ridge regression: Biased estimation for nonorthogonal problems,Technometrics 12 (1970), no. 1, 55-67.Google Scholar

[HL76] G. T., Herman and A., Lent, Quadratic optimization for image reconstruction. I,Computer Graphics and Image Processing 5 (1976), no. 3, 319-332.Google Scholar

[HO00] A., Hyvärinen and E., Oja, Independent component analysis: Algorithms and applications, Neural Networks 13 (2000), no. 4, 411-430.Google Scholar

[Hör80] L., Hörmander, The Analysis of Linear Differential Operators I: Distribution Theoryand Fourier Analysis, 2nd edn., Springer, 1980.Google Scholar

[Hör05] The Analysis of Linear Partial Differential Operators II. Differential Operators with Constant Coefficients. Classics in mathematics, Springer, 2005.

[HP76] M., Hamidi and J., Pearl, Comparison of the cosine and Fourier transforms of Markov-1 signals,IEEE Transactions on Acoustics, Speech and Signal Processing 24 (1976), no. 5, 428-429.Google Scholar

[HS04] T., Hida and S., Si, An Innovation Approach to Random Fields: Application of White Noise Theory,World Scientific, 2004.Google Scholar

[HS08] Lectures on White Noise Functionals,World Scientific, 2008.

[HSS08] T., Hofmann, B., Schölkopf, and A. J., Smola, Kernel methods in machine learning,Annals of Statistics 36 (2008), no. 3, 1171-1220.Google Scholar

[HT02] D. W., Holdsworth and M. M., Thornton, Micro-CT in small animal and specimen imaging,Trends in Biotechnology 20 (2002), no. 8, S34-S39.Google Scholar

[Hun77] B. R., Hunt, Bayesian methods in nonlinear digital image restoration, IEEE Transactions on Computers C-26 (1977), no. 3, 219-229.Google Scholar

[HW85] K. M., Hanson and G. W., Wecksung, Local basis-function approach to computed tomography,Applied Optics 24 (1985), no. 23, 4028-4039.Google Scholar

[HY00] M., Hansen and B., Yu, Wavelet thresholding via MDL for natural images,IEEE Transactions on Information Theory 46 (2000), no. 5, 1778-1788.Google Scholar

[Itô54] K., Itô, Stationary random distributions,Kyoto Journal of Mathematics 28 (1954), no. 3, 209-223.Google Scholar

[Itô84] Foundations of Stochastic Differential Equations in Infinite-Dimensional Spaces, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 47, Society for Industrial and Applied Mathematics (SIAM), 1984.

[Jac01] N., Jacob, Pseudo Differential Operators & Markov Processes, Vol.1: Fourier Analysis and Semigroups,World Scientific, 2001.Google Scholar

[Jai79] A. K., Jain, A sinusoidal family of unitary transforms,IEEE Transactions on Pattern Analysis and Machine Intelligence 1 (1979), no. 4, 356-365.Google Scholar

[Jai89] Fundamentals of Digital Image Processing,Prentice-Hall, 1989.

[JMR01] S., Jaffard, Y., Meyer, and R. D., Ryan, Wavelets: Tools for Science and Technology,SIAM, 2001.Google Scholar

[JN84] N. S., Jayant and P., Noll, Digital Coding of Waveforms: Principles and Application to Speech and Video Coding,Prentice-Hall, 1984.Google Scholar

[Joh66] S., Johansen, An application of extreme point methods to the representation of infinitely divisible distributions,Probability Theory and Related Fields 5 (1966), 304-316.Google Scholar

[Kai70] T., Kailath, The innovations approach to detection and estimation theory,Proceedings of the IEEE 58 (1970), no. 5, 680-695.Google Scholar

[Kal06] W. A., Kalender, X-ray computed tomography,Physics in Medicine and Biology 51 (2006), no. 13, R29.Google Scholar

[Kap62] W., Kaplan, Operational Methods for Linear Systems,Addison-Wesley, 1962.Google Scholar

[KBU12] U., Kamilov, E., Bostan, and M., Unser, Wavelet shrinkage with consistent cycle spinning generalizes total variation denoising,IEEE Signal Processing Letters 19 (2012), no. 4, 187-190.Google Scholar

[KFL01] F. R., Kschischang, B. J., Frey, and H.-A., Loeliger, Factor graphs and the sumproduct algorithm,IEEE Transactions on Information Theory 47 (2001), no. 2, 498-519.Google Scholar

[Khi34] A., Khintchine, Korrelationstheorie der stationären stochastischen Prozesse,Mathematische Annalen 109 (1934), no. 1, 604-615.Google Scholar

[Khi37a] A new derivation of one formula by P., Lévy, Bulletin of Moscow State University, I (1937), no. 1,1-5.

[Khi37b] Zur Theorie der unbeschränkt teilbaren Verteilungsgesetze,Recueil Mathématique (Matematiceskij Sbornik) 44 (1937), no. 2, 79-119.

[KKBU12] A., Kazerouni, U. S., Kamilov, E., Bostan, and M., Unser, Bayesian denoising: From MAP to MMSE using consistent cycle spinning,IEEESignal Processing Letters 20 (2012), no. 3, 249-252.Google Scholar

[KMU11] H., Kirshner, S., Maggio, and M., Unser, A sampling theory approach for continuous ARMA identification,IEEE Transactions on Signal Processing 59 (2011), no. 10, 46204634.Google Scholar

[Kol35] A. N., Kolmogoroff, La transformation de Laplace dans les espaces linéaires,Comptes Rendus de l'Académie des Sciences 200 (1935), 1717-1718, Note de A. N. Kolmogoroff, présentée par Jacques Hadamard.Google Scholar

[Kol40] Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum,Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS 26 (1940), no. 2, 115-118.

[Kol41] A. N., Kolmogorov, Stationary sequences in Hilbert space,Vestnik Moskovskogo Universiteta, Seriya 1: Matematika, Mekhanika 2 (1941), no. 6, 1-40.Google Scholar

[Kol56] Foundations of the Theory of Probability, 2nd English edn., Chelsea Publishing, 1956.

[Kol59] A note on the papers of R. A. Minlos and V. Sazonov, Theory of Probability and Its Applications 4 (1959), no. 2, 221-223.

[KPAU13] U. S., Kamilov, P., Pad, A., Amini, and M., Unser, MMSE estimation of sparse Lévy processes,IEEE Transactions on Signal Processing 61 (2013), no. 1, 137-147.Google Scholar

[Kru70] V. M., Kruglov, A note on infinitely divisible distributions,Theory of Probability and Its Applications 15 (1970), no. 2, 319-324.Google Scholar

[KU06] I., Khalidov and M., Unser, From differential equations to the construction of new wavelet-like bases, IEEE Transactions on Signal Processin 54 (2006), no. 4, 1256-1267.Google Scholar

[KUW13] I., Khalidov, M., Unser, and J. P., Ward, Operator-like bases of L2(Rd), Journal of Fourier Analysis and Applications 19, (2013), no. 6, 1294-1322.Google Scholar

[KV90] N. B., Karayiannis and A. N., Venetsanopoulos, Regularization theory in image restoration: The stabilizing functional approach,IEEE Transactions on Acoustics, Speech and Signal Processing 38 (1990), no. 7, 1155-1179.Google Scholar

[KW70] G., Kimeldorf and G., Wahba, A correspondence between Bayesian estimation on stochastic processes and smoothing by splines,Annals of Mathematical Statistics 41 (1970), no. 2, 495-502.Google Scholar

[Lat98] B. P., Lathy, Signal Processing and Linear Systems,Berkeley-Cambridge Press, 1998.Google Scholar

[LBU07] F., Luisier, T., Blu, and M., Unser, A new SURE approach to image denoising: Interscale orthonormal wavelet thresholding,IEEE Transactions on Image Processing 16 (2007), no. 3, 593-606.Google Scholar

[LC47] L., Le Cam, Un instrument d'étude des fonctions aléatoires: la fonctionnelle caractéristique,Comptes Rendus de l'Académie des Sciences 224 (1947), no. 3, 710-711.Google Scholar

[LDP07] M., Lustig, D. L., Donoho, and J. M., Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging,Magnetic Resonance in Medicine 58 (2007), no. 6, 1182-1195.Google Scholar

[Lév25] P., Lévy, Calcul des Probabilités,Gauthier-Villars, 1925.Google Scholar

[Lév34] Sur les intégrales dont les éléments sont des variables aléatoires indépendantes,Annali della Scuola Normale Superiore di Pisa: Classe di Scienze 3 (1934), no. 3-4, 337-366.

[Lév54] Le Mouvement Brownien, Mémorial des Sciences Mathématiques, vol. CXXVI, Gauthier-Villars, 1954.

[Lév65] Processus Stochastiques et Mouvement Brownien, 2nd edn., Gauthier-Villars, 1965.

[Lew90] R. M., Lewitt, Multidimensional digital image representations using generalized Kaiser Bessel window functions,Journal of the Optical Society of America A 7 (1990), no. 10, 1834-1846.Google Scholar

[LFB05] V., Lucic, F., Förster, and W., Baumeister, Structural studies by electron tomography: From cells to molecules,Annual Review of Biochemistry 74 (2005), 833-865.Google Scholar

[Loè73] M., Loève, Paul, Lévy, 1886-1971, Annals of Probability 1 (1973), no. 1,1-8.

[Loe04] H.-A., Loeliger, An introduction to factor graphs,IEEE Signal Processing Magazine 21 (2004), no. 1, 28-41.Google Scholar

[LR78] A. V., Lazo and P., Rathie, On the entropy of continuous probability distributions,IEEE Transactions on Information Theory 24 (1978), no. 1, 120-122.Google Scholar

[Luc74] L. B., Lucy, An iterative technique for the rectification of observed distributions,The Astronomical Journal 6 (1974), no. 6, 745-754.Google Scholar

[Mal56] B., Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution,Annales de l'Institut Fourier 6 (1956), 271-355.Google Scholar

[Mal89] S. G., Mallat, A theory of multiresolution signal decomposition: The wavelet representation,IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (1989), no. 7, 674-693.Google Scholar

[Mal98] S., Mallat, A Wavelet Tour of Signal Processing,Academic Press, 1998.Google Scholar

[Mal09] A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn., Academic Press, 2009.

[Man63] B. B., Mandelbrot, The variation of certain speculative prices,The Journal of Business 36 (1963), no. 4, 393-413.Google Scholar

[Man82] The Fractal Geometry of Nature,Freeman, 1982.

[Man01] Gaussian Self-Affinity and Fractals,Springer, 2001.

[Mar05] R., Martin, Speech enhancement based on minimum mean-square error estimationand supergaussian priors,IEEE Transactions on Speech and Audio Processing 13 (2005), no. 5, 845-856.Google Scholar

[Mat63] G., Matheron, Principles of geostatistics,Economic Geology 58 (1963), no. 8, 1246-1266.Google Scholar

[Mey90] Y., Meyer, Ondelettes et Opérateurs I: Ondelettes,Hermann, 1990.Google Scholar

[MG01] D., Mumford and B., Gidas, Stochastic models for generic images,Quarterly of Applied Mathematics 59 (2001), no. 1, 85-112.Google Scholar

[Mic76] C., Micchelli, Cardinal L-splines, Studies in Spline Functions and Approximation Theory (S., Karlin, C., Micchelli, A., Pinkus, and I., Schoenberg, eds.), Academic Press, 1976, pp. 203-250.Google Scholar

[Mic86] Interpolation of scattered data: Distance matrices and conditionally positive definite functions,Constructive Approximation 2 (1986), no. 1, 11-22.

[Min63] R. A., Minlos, Generalized Random Processes and Their Extension to a Measure, Selected Translations in Mathematical Statististics and Probability, vol. 3, American Mathematical Society, 1963, pp. 291-313.Google Scholar

[Miy61] K., Miyasawa, An empirical Bayes estimator of the mean of a normal population,Bulletin de l'Institut International de Statistique 38 (1961), no. 4, 181-188.Google Scholar

[MKCC99] J. G., McNally, T., Karpova, J., Cooper, and J. A., Conchello, Three-dimensional imaging by deconvolution microscopy,Methods 19 (1999), no. 3, 373-385.Google Scholar

[ML99] P., Moulin and J., Liu, Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors,IEEE Transactions on Information Theory 45 (1999), no. 3, 909-919.Google Scholar

[MN90a] W. R., Madych and S. A., Nelson, Multivariate interpolation and conditionally positive definite functions. II,Mathematics of Computation 54 (1990), no. 189, 211-230.Google Scholar

[MN90b] Polyharmonic cardinal splines,Journal of Approximation Theory 60 (1990), no. 2, 141-156.

[MP86] S. G., Mikhlin and S., Prössdorf, Singular Integral Operators,Springer, 1986.Google Scholar

[MR06] F., Mainardi and S., Rogosin, The origin of infinitely divisible distributions: From de Finetti's problem to Lévy-Khintchine formula,Mathematical Methods in Economics and Finance 1 (2006), no. 1, 7-55.Google Scholar

[MVN68] B. B., Mandelbrot and J. W., VanNess, Fractional Brownian motions, fractional noises and applications,SIAM Review 10 (1968), no. 4, 422-437.Google Scholar

[Mye92] D. E., Myers, Kriging, cokriging, radial basis functions and the role of positive definiteness,Computers and Mathematics with Applications 24 (1992), no. 12, 139-148.Google Scholar

[Nat84] F., Natterer, The Mathematics of Computed Tomography,John Wiley & Sons, 1984.Google Scholar

[New75] D. J., Newman, A simple proof of Wiener's1/f theorem,Proceedings of the American Mathematical Society 48 (1975), no. 1, 264-265.Google Scholar

[Nik07] M., Nikolova, Model distortions in Bayesian MAP reconstruction,Inverse Problems and Imaging 1 (2007), no. 2, 399-422.Google Scholar

[OF96a] B. A., Olshausen and D. J., Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images,Nature 381 (1996), no. 6583, 607-609.Google Scholar

[OF96b] Natural image statistics and efficient coding,Network: Computation in Neural Systems 7 (1996), no. 2, 333-339.

[0ks07] B., Øksendal, Stochastic Differential Equations, 6th edn., Springer, 2007.Google Scholar

[OSB99] A. V., Oppenheim, R. W., Schafer, and J. R., Buck, Discrete-Time Signal Processing,Prentice Hall, 1999.Google Scholar

[PAP72] J., Pearl, H. C., Andrews, and W., Pratt, Performance measures for transform data coding,IEEE Transactions on Communications 20 (1972), no. 3, 411-415.Google Scholar

[Pap91] A., Papoulis, Probability, Random Variables, and Stochastic Processes,McGraw-Hill, 1991.Google Scholar

[PBE01] M., Persson, D., Bone, and H., Elmqvist, Total variation norm for three dimensional iterative reconstruction in limited view angle tomography,Physics in Medicine and Biology 46 (2001), no. 3, 853.Google Scholar

[Pet05] M., Petit, L'équation de Kolmogoroff: Vie et Mort de Wolfgang Doeblin, un Génie dans la Tourmente Nazie,Gallimard, 2005.Google Scholar

[PHBJ+01] E., Perrin, R., Harba, C., Berzin-Joseph, I., Iribarren, and A., Bonami, nth-order fractional Brownian motion and fractional Gaussian noises,IEEE Transactions on Signal Processing 49 (2001), no. 5, 1049-1059.Google Scholar

[Pie72] A., Pietsch, Nuclear Locally Convex Spaces,Springer, 1972.Google Scholar

[PM62] D. P., Petersen and D., Middleton, Sampling and reconstruction of wave-number limited functions in n-dimensional Euclidean spaces,Information and Control 5 (1962), no. 4, 279-323.Google Scholar

[PMC93] C., Preza, M. I., Miller, and J.-A., Conchello, Image reconstruction for 3D light microscopy with a regularized linear method incorporating a smoothness prior, Proceedings of the IS&T/SPIE Symposium on Electronic Imaging Science and Technology (San Jose, CA, January 1993), vol. 1905, SPIE 1993, pp. 129-139.Google Scholar

[PP06] A., Pizurica and W., Philips, Estimating the probability of the presence of a signal of interest in multiresolution single- and multi band image denoising,IEEE Transactions on Image Processing 15 (2006), no. 3, 654-665.Google Scholar

[PPLV02] B., Pesquet-Popescu and J. Lévy, Véhel, Stochastic fractal models for image processing,IEEE Signal Processing Magazine 19 (2002), no. 5, 48-62.Google Scholar

[PR70] B. L. S. Prakasa, Rao, Infinitely divisible characteristic functionals on locally convex topological vector spaces,Pacific Journal of Mathematics 35 (1970), no. 1, 221-225.Google Scholar

[Pra91] W. K., Pratt, Digital Image Processing,John Wiley & Sons, 1991.Google Scholar

[Pro04] P., Protter, Stochastic Integration and Differential Equations,Springer, 2004.Google Scholar

[Pru06] K. P., Pruessmann, Encoding and reconstruction in parallel MRI,NMR in Biomedicine 19 (2006), no. 3, 288-299.Google Scholar

[PSV09] X., Pan, E. Y., Sidky, and M., Vannier, Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?,Inverse Problems 25 (2009), no. 12, 123009.Google Scholar

[PSWS03] J., Portilla, V., Strela, M. J., Wainwright, and E. P., Simoncelli, Image denoising using scale mixtures of Gaussians in the wavelet domain,IEEE Transactions on Image Processing 12 (2003), no. 11, 1338-1351.Google Scholar

[PU13] P., Pad and M., Unser, On the optimality of operator-like wavelets for sparse AR(1) processes, Proceedings of the 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'13) (Vancouver, BC, Canada, May 26-31, 2013), IEEE, 2013, pp. 5598-5602.Google Scholar

[PWSB99] K. P., Pruessmann, M., Weiger, M. B., Scheidegger, and P., Boesiger, SENSE: Sensitivity encoding for fast MRI,Magnetic Resonance in Medicine 42 (1999), no. 5, 952-962.Google Scholar

[Rab92a] C., Rabut, Elementary m-harmonic cardinal B-splines, Numerical Algorithms 2 (1992), no. 2, 39-61.Google Scholar

[Rab92b] High level m-harmonic cardinal B-splines,Numerical Algorithms 2 (1992), 63-84.

[Ram69] B., Ramachandran, On characteristic functions and moments,Sankhya: The Indian Journal of Statistics, Series A 31 (1969), no. 1, 1-12.Google Scholar

[RB94] D. L., Ruderman and W., Bialek, Statistics of natural images: Scaling in the woods,Physical Review Letters 73 (1994), no. 6, 814-818.Google Scholar

[RBFK11] L., Ritschl, F., Bergner, C., Fleischmann, and M., Kachelrieß, Improved total variation-based CT image reconstruction applied to clinical data,Physics in Medicine and Biology 56 (2011), no. 6, 1545.Google Scholar

[RF11] S., Ramani and J. A., Fessler, Parallel MR image reconstructionusing augmented Lagrangian methods,IEEE Transactions on Medical Imaging 30 (2011), no. 3, 694-706.Google Scholar

[Ric72] W., Richardson, Bayesian-based iterative method of image restoration,Journal of the Optical Society of America 62 (1972), no. 1, 55-59.Google Scholar

[Ric77] J., Rice, On generalized shot noise,Advances in Applied Probability 9 (1977), no. 3, 553-565.Google Scholar

[RL71] G. N., Ramachandran and A. V., Lakshminarayanan, Three-dimensional reconstruction from radiographs and electron micrographs: Application of convolutions instead of Fourier transforms,Proceedings of the National Academy of Sciences 68 (1971), no. 9, 2236-2240.Google Scholar

[ROF92] L. I., Rudin, S., Osher, and E., Fatemi, Nonlinear total variation based noise removal algorithms,Physica D 60 (1992), no. 1-4, 259-268.Google Scholar

[Ron88] A., Ron, Exponential box splines,Constructive Approximation 4 (1988), no. 1, 357-378.Google Scholar

[RS08] M., Raphan and E. P., Simoncelli, Optimal denoising in redundant representations,IEEE Transactions on Image Processing 17 (2008), no. 8, 1342-1352.Google Scholar

[RU06] S., Ramani and M., Unser, Matérn B-splines and the optimal reconstruction of signals,IEEE Signal Processing Letters 13 (2006), no. 7, 437-440.Google Scholar

[Rud73] W., Rudin, Functional analysis,McGraw-Hill Series in Higher Mathematics, McGraw-Hill, 1973.Google Scholar

[Rud97] D. L., Ruderman, Origins of scaling in natural images,Vision Research 37 (1997), no. 23, 3385-3398.Google Scholar

[RVDVBU08] S., Ramani, D., Van De Ville, T., Blu, and M., Unser, Nonideal sampling and regularization theory,IEEE Transactions on Signal Processing 56 (2008), no. 3, 1055-1070.Google Scholar

[SA96] E. P., Simoncelli and E. H., Adelson, Noise removal via Bayesian wavelet coring, Proceedings of the IEEE International Conference on Image Processing (ICIP2010), (Lausanne, Switzerland September 16-19, 1996), vol. 1, IEEE, 1996, pp. 379-382.Google Scholar

[Sat94] K.-I., Sato, Lévy Processes and Infinitely Divisible Distributions,Chapman & Hall, 1994.Google Scholar

[Sch38] I. J., Schoenberg, Metric spaces and positive definite functions,Transactions of the American Mathematical Society 44 (1938), no. 3, 522-536.Google Scholar

[Sch46] Contribution to the problem of approximation of equidistant data by analytic functions,Quarterly of Applied Mathematics 4 (1946), 45-99, 112-141.

[Sch66] L., Schwartz, Théorie des Distributions,Hermann, 1966.Google Scholar

[Sch73a] I. J., Schoenberg, Cardinal Spline Interpolation,Society of Industrial and Applied Mathematics, 1973.Google Scholar

[Sch73b] L., Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Studies in Mathematics, vol. 6, Tata Institute of Fundamental Research, Bombay Oxford University Press, 1973.Google Scholar

[Sch81a] L. L., Schumaker, Spline Functions: Basic Theory,John Wiley & Sons, 1981.Google Scholar

[Sch81b] L., Schwartz, Geometry and Probability in Banach Spaces,Lecture Notes in Mathematics, vol. 852, Springer, 1981.Google Scholar

[Sch88] I. J., Schoenberg, A Brief Account of My Life and Work, Selected papers (C. de Boor, ed.), vol. 1, Birkhäuser, 1988, pp. 1-10.Google Scholar

[Sch99] H. H., Schaefer, Topological Vector Spaces, 2nd edn., Graduate Texts in Mathematics, vol. 3, Springer, 1999.Google Scholar

[SDFR13] J.-L., Starck, D. L., Donoho, M. J., Fadili, and A., Rassat, Sparsity and the Bayesian perspective,Astronomyand Astrophysics 552 (2013), A133.Google Scholar

[SF71] G., Strang and G., Fix, A Fourier analysis of the finite element variational method, Constructive Aspects of Functional Analysis, Edizioni Cremonese, 1971, pp. 793-840.Google Scholar

[Sha93] J., Shapiro, Embedded image coding using zerotrees of wavelet coefficients,IEEE Transactions on Acoustics, Speech and Signal Processing 41 (1993), no. 12, 3445-3462.Google Scholar

[Sil99] B. W., Silverman, Wavelets in statistics: Beyond the standard assumptions,Philosophical Transactions: Mathematical, Physical and Engineering Sciences 357 (1999), no. 1760, 2459-2473.Google Scholar

[SLG02] A., Srivastava, X., Liu, and U., Grenander, Universal analytical forms for modeling image probabilities,IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (2002), no. 9, 1200-1214.Google Scholar

[SLSZ03] A., Srivastava, A. B., Lee, E. P., Simoncelli, and S.-C., Zhu, Onadvances instatistical modeling of natural images,Journal of Mathematical Imaging and Vision 18 (2003), 17-33.Google Scholar

[SO01] E. P., Simoncelli and B. A., Olshausen, Natural image statistics and neural representation,Annual Review of Neuroscience 24 (2001), 1193-1216.Google Scholar

[Sob36] S., Soboleff, Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales, Recueil Mathématique (Matematiceskij Sbornik) 1(43) (1936), no. 1,39-72.Google Scholar

[SP08] E. Y., Sidky and X., Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,Physics in Medicine and Biology 53 (2008), no. 17, 4777.Google Scholar

[SPM02] J.-L., Starck, E., Pantin, and F., Murtagh, Deconvolution in astronomy: A review,Publications of the Astronomical Society of the Pacific 114 (2002), no. 800, 1051-1069.Google Scholar

[SS02] L., Sendur and I. W., Selesnick, Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency,IEEE Transactions on Signal Processing 50 (2002), no. 11, 2744-2756.Google Scholar

[ST94] G., Samorodnitsky and M. S., Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance,Chapman & Hall, 1994.Google Scholar

[Ste76] J., Stewart, Positive definite functions and generalizations: An historical survey,Rocky Mountain Journal of Mathematics 6 (1976), no. 3, 409-434.Google Scholar

[Ste81] C., Stein, Estimation of the mean of a multivariate normal distribution,Annals of Statistics 9 (1981), no. 6, 1135-1151.Google Scholar

[SU12] Q., Sun and M., Unser, Left inverses of fractional Laplacian and sparse stochastic processes,Advances in Computational Mathematics 36 (2012), no. 3, 399-441.Google Scholar

[Sun93] X., Sun, Conditionally positive definite functions and their application to multivariate interpolations,Journal of Approximation Theory 74 (1993), no. 2, 159-180.Google Scholar

[Sun07] Q., Sun, Wiener's lemma for infinite matrices,Transactions of the American Mathematical Society 359 (2007), no. 7, 3099-3123.Google Scholar

[SV67] M. H., Schultz and R. S., Varga, L-splines,Numerische Mathematik 10 (1967), no. 4, 345-369.Google Scholar

[SVH03] F. W., Steutel and K., Van Harn, Infinite Divisibility of Probability Distributions on the Real Line,Marcel Dekker, 2003.Google Scholar

[SW71] E. M., Stein and G., Weiss, Introduction to Fourier Analysis on Euclidean Spaces,Princeton University Press, 1971.Google Scholar

[TA77] A. N., Tikhonov and V. Y., Arsenin, Solution of Ill-Posed Problems, Winston & Sons, 1977.Google Scholar

[Taf11] P. D., Tafti, Self-similar vector fields, unpublished Ph.D. thesis, bcole Polytechnique Fédérate de Lausanne (2011).Google Scholar

[Tay75] S. J., Taylor, Paul Lévy,Bulletin of the London Mathematical Society 7 (1975), no. 3, 300-320.Google Scholar

[TBU00] P., Thévenaz, T., Blu, and M., Unser, Image interpolation and resampling, >Handbook of Medical Imaging, Processing and Analysis (I. N., Bankman, ed.), Academic Press, 2000, pp. 393-420.

[TH79] H. J., Trussell and B. R., Hunt, Improved methods of maximum a posteriori restoration,IEEETransactions on Computers 100 (1979), no. 1, 57-62.Google Scholar

[Tib96] R., Tibshirani, Regression shrinkage and selection via the Lasso,Journal of the Royal Statistical Society, Series B 58 (1996), no. 1, 265-288.Google Scholar

[Tik63] A. N., Tikhonov, Solution of incorrectly formulated problems and the regularization method,Soviet Mathematics 4 (1963), 1035-1038.Google Scholar

[TM09] J., Trzasko and A., Manduca, Highly undersampled magnetic resonance image reconstruction via homotopic £o-mmimization,IEEE Transactions on Medical Imaging 28 (2009), no. 1, 106-121.Google Scholar

[TN95] G. A., Tsihrintzis and C. L., Nikias, Performance of optimum and suboptimum receivers inthe presence of impulsive noise modeled as analpha-stable process,IEEE Transactions on Communications 43 (1995), no. 234, 904 -914.Google Scholar

[TVDVU09] P. D., Tafti, D., Van De Ville, and M., Unser, Invariances, Laplacian-like wavelet bases, and the whitening of fractal processes,IEEE Transactions on Image Processing 18 (2009), no. 4, 689-702.Google Scholar

[UAE92] M., Unser, A., Aldroubi, and M., Eden, On the asymptotic convergence of B-spline wavelets to Gabor functions,IEEE Transactions on Information Theory 38 (1992), no. 2, 864-872.Google Scholar

[UAE93] A family of polynomial spline wavelet transforms,Signal Processing 30 (1993), no. 2, 141-162.

[UB00] M., Unser and T., Blu, Fractional splines and wavelets,SIAM Review 42 (2000), no. 1, 43-67.Google Scholar

[UB03] Wavelet theory demystified,IEEE Transactions on Signal Processing 51 (2003), no. 2, 470-483.

[UB05a] Cardinal exponential splines, Part I: Theory and filtering algorithms,IEEE Transactions on Signal Processing 53 (2005), no. 4, 1425-1449.

[UB05b] Generalized smoothing splines and the optimal discretization of the Wiener filter,IEEE Transactions on Signal Processing 53 (2005), no. 6, 2146-2159.

[UB07] Self-similarity, Part I: Splines and operators,IEEE Transactions on Signal Processing 55 (2007), no. 4, 1352-1363.

[Uns84] M., Unser, On the approximation of the discrete Karhunen-Loève transform for stationary processes,Signal Processing 7 (1984), no. 3, 231-249.Google Scholar

[Uns93] On the optimality of ideal filters for pyramid and wavelet signal approximation,IEEE Transactions on Signal Processing 41 (1993), no. 12, 3591-3596.

[Uns99] Splines: A perfect fit for signal and image processing,IEEE Signal Processing Magazine 16 (1999), no. 6, 22-38.

[Uns00] Sampling: 50 years after Shannon,Proceedings of the IEEE 88 (2000), no. 4, 569-587.

[Uns05] Cardinal exponential splines, Part II: Think analog, act digital,IEEE Transactions on Signal Processing 53 (2005), no. 4, 1439-1449.

[UT11] M., Unser and P. D., Tafti, Stochastic models for sparse and piecewise-smooth signals,IEEETransactions on Signal Processing 59 (2011), no. 3, 989-1005.Google Scholar

[UTAK14] M., Unser, P. D., Tafti, A., Amini, and H., Kirshner, A unified formulation of Gaussian vs. sparse stochastic processes, Part II: Discrete-domain theory,IEEE Transactions on Information Theory 60 (2014), no. 5, 3036-3051.Google Scholar

[UTS14] M., Unser, P. D., Tafti, and Q., Sun, A unified formulation of Gaussian vs. sparse stochastic processes, Part I: Continuous-domain theory,IEEE Transactions on Information Theory 60 (2014), no. 3, 1361-1376.Google Scholar

[VAVU06] C., Vonesch, F., Aguet, J.-L., Vonesch, and M., Unser, The colored revolution of bioimaging,IEEE Signal Processing Magazine 23 (2006), no. 3, 20-31.Google Scholar

[VBB+02] G. M., Viswanathan, F., Bartumeus, S. V., Buldyrev, J., Catalan, U. L., Fulco, S., Havlin, M.G., E da Luz, M. L., Lyra, E.P., Raposo, and H.E., Stanley, Lévy flight random searches in biological phenomena,Physica A: Statistical Mechanics and Its Applications 314 (2002), no. 1-4, 208-213.Google Scholar

[VBU07] C., Vonesch, T., Blu, and M., Unser, Generalized Daubechies wavelet families,IEEE Transactions on Signal Processing 55 (2007), no. 9, 4415-4429.Google Scholar

[VDVBU05] D., Van De Ville, T., Blu, and M., Unser, Isotropic polyharmonic B-splines: Scaling functions and wavelets,IEEE Transactions on Image Processing 14 (2005), no. 11, 1798-1813.Google Scholar

[VDVFHUB10] D., Van De Ville, B., Forster-Heinlein, M., Unser, and T., Blu, Analytical footprints: Compact representation of elementary singularities in wavelet bases,IEEE Transactions on Signal Processing 58 (2010), no. 12, 6105-6118.Google Scholar

[vKvVVvdV97] G. M. P., van Kempen, L. J., van Vliet, P. J., Verveer, and H. T. M., van der Voort, A quantitative comparison of image restoration methods for confocal microscopy,Journal of Microscopy 185 (1997), no. 3, 345-365.Google Scholar

[VMB02] M., Vetterli, P., Marziliano, and T., Blu, Sampling signals with finite rate of innovation,IEEE Transactions on Signal Processing 50 (2002), no. 6, 1417-1428.Google Scholar

[VU08] C., Vonesch and M., Unser, Afastthresholded Landweber algorithm for waveletregularized multidimensional deconvolution,IEEE Transactions on Image Processing 17 (2008), no. 4, 539-549.Google Scholar

[VU09] A fast multilevel algorithm for wavelet-regularized image restoration,IEEE Transactions on Image Processing 18 (2009), no. 3, 509-523.

[Wag09] P., Wagner, A new constructive proof of the Malgrange-Ehrenpreis theorem,American Mathematical Monthly 116 (2009), no. 5, 457-462.Google Scholar

[Wah90] G., Wahba, Spline Models for Observational Data,Society for Industrial and Applied Mathematics, 1990.Google Scholar

[Wen05] H., Wendland, Scattered Data Approximations,Cambridge University Press, 2005.Google Scholar

[Wie30] N., Wiener, Generalized harmonic analysis,Acta Mathematica 55 (1930), no. 1, 117-258.Google Scholar

[Wie32] Tauberian theorems,Annals of Mathematics 33 (1932), no. 1, 1-100.

[Wie64] Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications,MIT Press, 1964.

[WLLL06] J., Wang, T., Li, H., Lu, and Z., Liang, Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography,IEEE Transactions on Medical Imaging 25 (2006), no. 10, 1272-1283.Google Scholar

[WM57] N., Wiener and P., Masani, The prediction theory of multivariate stochastic processes,Acta Mathematica 98 (1957), no. 1, 111-150.Google Scholar

[WN10] D., Wipf and S., Nagarajan, Iterative reweighted and methods for finding sparse solutions,IEEE Journal of Selected Topics in Signal Processing 4 (2010), no. 2, 317-329.Google Scholar

[Wol71] S. J., Wolfe, On moments of infinitely divisible distribution functions,The Annals of Mathematical Statistics 42 (1971), no. 6, 2036-2043.Google Scholar

[Wol78] On the unimodality of infinitely divisible distribution functions,Probability Theory and Related Fields 45 (1978), no. 4, 329-335.

[WYHJC91] J. B., Weaver, X., Yansun, D. M., Healy Jr., and L. D., Cromwell, Filtering noise from images with wavelet transforms,Magnetic Resonance in Medicine 21 (1991), no. 2, 288-295.Google Scholar

[WYYZ08] Y. L., Wang, J. F., Yang, W. T., Yin, and Y., Zhang, A new alternating minimization algorithm for total variation image reconstruction,SIAM Journal on Imaging Sciences 1 (2008), no. 3, 248-272.Google Scholar

[XQJ05] X. Q., Zhang and F., Jacques, Constrained total variation minimization and application in computerized tomography, Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, vol. 3757, Springer, 2005, pp. 456-472.Google Scholar

[Yag86] A. M., Yaglom, Correlation Theory of Stationary and Related Random Functions I: Basic Results,Springer, 1986.Google Scholar

[Zem10] A. H., Zemanian, Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications,Dover, 2010.Google Scholar