Outer Product Expansions and Their Uses in Digital Image Processing

This paper is intended as a tutorial review of certain digital image processing transform techniques utilizing the notion of outer product expansions. Examples from Fourier, Walsh, Haar, and other well known transforms are reviewed in the notation of matrix-vector outer products; and implementation of the singular value decomposition (SVD) of large sized images is presented. The use of the SVD as an aid in image restoration utilizing the pseudoinverses is presented. Conditions on the point spread matrix are investigated in the light of singular value decomposition, Kronecker products, and general imaging conditions.