TY - JOUR
T1 - Kronecker Product Approximations forImage Restoration with Reflexive Boundary Conditions
AU - Nagy, James G.
AU - Ng, Michael K.
AU - Perrone, Lisa
N1 - This work was supported by the National Science Foundation under grant DMS 00-75239.
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong ([email protected]). The research of this author was supported in part by RGC grants 7132/00P and 7130/02P and HKU CRCG grants 10203501, 10203907, and 10204437.
Publisher Copyright:
© 2004 Society for Industrial and Applied Mathematics.
PY - 2003/1
Y1 - 2003/1
N2 - Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. When reflexive (Neumann) boundary conditions are used, the coefficient matrix is a combination of Toeplitz and Hankel matrices. Kronecker products also occur, but this structure is not obvious from measured data. In this paper we discuss a scheme for computing a (possibly approximate) Kronecker product decomposition of structured matrices in image processing, which extends previous work by Kamm and Nagy [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 155--172] to a wider class of image restoration problems.
AB - Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. When reflexive (Neumann) boundary conditions are used, the coefficient matrix is a combination of Toeplitz and Hankel matrices. Kronecker products also occur, but this structure is not obvious from measured data. In this paper we discuss a scheme for computing a (possibly approximate) Kronecker product decomposition of structured matrices in image processing, which extends previous work by Kamm and Nagy [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 155--172] to a wider class of image restoration problems.
KW - image restoration
KW - Kronecker product
KW - singular value decomposition
UR - http://www.scopus.com/inward/record.url?scp=3142661848&partnerID=8YFLogxK
U2 - 10.1137/S0895479802419580
DO - 10.1137/S0895479802419580
M3 - Journal article
AN - SCOPUS:3142661848
SN - 0895-4798
VL - 25
SP - 829
EP - 841
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 3
ER -