Title :
Outer Product Expansions and Their Uses in Digital Image Processing
Author :
Andrews, Harry C. ; Patterson, Claude L.
Author_Institution :
Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90007.
Abstract :
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.
Keywords :
Digital images; Image analysis; Image coding; Image motion analysis; Image processing; Image restoration; Image storage; Image texture analysis; Matrix decomposition; Singular value decomposition; Fourier transform; Haar transform; Walsh transform; image processing outer products; pseudoinverses; singular value decomposition;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.1976.5009228
