Introductory remarks

In this chapter, two different classes of image restoration approaches are presented. Though the stress is placed on images corrupted by so-called “salt and pepper” noise, represented by the mixture distribution model, the methodologies presented here are applicable if the background noise deviates significantly from Gaussian. The image restoration is accomplished in two stages. In the first stage, edge detectors introduced in Chapter 4 are used as preprocessors to establish the local orientation of potential edge points. In the second stage, some form of Robbins–Monro type recursive estimator (see Chapter 8) is applied to remove the undesirable corruption of the image. Alternately, the badly corrupted pixels are replaced by estimated values based on the missing value approach. Based on extensive simulation studies in various noise environments, the edge detection preprocessors that were found to be of practical use are 5 x 5 Graeco-Latin squares (GLS) (see Section 4.5.2) and 6 x 7 Youden squares (YS) (see Section 3.7.2).

Many image restoration procedures, such as averaging and median filters, represent a smoothing process and will cause blurring of the restored image. The averaging filter represents a sample mean and is not robust in salt and pepper noise because of the high variance of the latter.