Kronecker Product Approximations for Image Restoration with Reflexive Boundary Conditions

Authors:
James G. Nagy;Michael K. Ng;Lisa Perrone
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2003

Citing 0
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Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides

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Conditional gradient Tikhonov method for a convex optimization problem in image restoration

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Abstract

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.