In many sensing and imaging problems, the object is covered by some medium that conceals or obscures its relevant features. The object may emit some wave, field, or stream of particles that penetrate the medium and may be observed by a detector. Alternatively, a wave, field, or stream of particles may be used as a probe that travels through the medium and is modified by the object before it travels back through the medium on its way to the detector. The challenge is to extract information about the subsurface target in the presence of the obscuring medium.

Subsurface imaging (SSI) problems arise in a wide range of areas: geophysical exploration or environmental remediation under the earth or the ocean, medical examination and diagnosis inside the body, basic studies of the biological processes inside the cell, and security inspections for explosives or contraband concealed in luggage. While these problems involve many sensing modalities (mechanical, acoustic, electric, magnetic, electromagnetic, optical, X-ray, electrons, or other particles), they all seek to infer internal structure from complex and distorted signals received outside the obscuring volume. They often employ similar physical and mathematical models and use similar computational and algorithmic methods.

This textbook introduces the field of subsurface imaging, its principles, methods, and applications, using a unifying framework that strives to integrate the diverse topics, which are often presented separately in different science and engineering textbooks or in various venues of the research literature.