Information-Theoretic Image Formation with Applications in Hyperspectral and Medical Imaging

Information theory plays a role in many aspects of imaging problems, from the problem definition, through the development of algorithms, to the implementation of those algorithms and performance quantification. While derivation of performance bounds is arguably the most fundamental contribution of information theory to imaging problems, development of algorithms based on information-theoretic criteria is also important. An important class of algorithms for imaging problem consists of alternating minimization algorithms. We discuss the derivation of alternating minimization algorithms that result from minimization of the I-divergence between two functions where the first function is restricted to a linear family and the second function is restricted to an exponential family. Many well known alternating minimization algorithms fit within this framework including algorithms for extracting endmembers in hyperspectral imaging and for forming images in transmission tomography. These two examples are discussed in detail.