Singular value decompositions and digital image processing

The use of singular value decomposition (SVD) techniques in digital image processing is of considerable interest for those facilities with large computing power and stringent imaging requirements. The SVD methods are useful for image as well as quite general point spread function (impulse response) representations. The methods represent simple extensions of the theory of linear filtering. Image enhancement examples will be developed illustrating these principles. The most interesting cases of image restoration are those which involve space variant imaging systems. The SVD, combined with pseudoinverse techniques, provides insight into these types of restorations. Illustrations of large scale N 2 × N 2 point spread function matrix representations are discussed along with separable space variant N 2 × N 2 point spread function matrix examples. Finally, analysis and methods for obtaining a pseudoinverse of separable space variant point spread functions (SVPSF's) are presented with a variety of object and imaging system dagradations.