Kronecker product and SVD approximations in image restoration
نویسندگان
چکیده
منابع مشابه
Kronecker Product and SVD Approximations inImage
Image restoration applications often result in ill-posed least squares problems involving large, structured matrices. One approach used extensively is to restore the image in the frequency domain, thus providing fast algorithms using ffts. This is equivalent to using a circulant approximation to a given matrix. Iterative methods may also be used eeectively by exploiting the structure of the mat...
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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. Wh...
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The goal of this work is the presentation of some new formats which are useful for the approximation of (large and dense) matrices related to certain classes of functions and nonlocal (integral, integrodifferential) operators, especially for high-dimensional problems. These new formats elaborate on a sum of few terms of Kronecker products of smaller-sized matrices (cf. [37, 38]). In addition to...
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In this paper, we propose a method to find the best Kronecker product approximation of the blurring operator which arises in three dimensional image restoration problems. We show that this problem can be reduced to a well known rank-1 approximation of the scaled three dimensional point spread function (PSF) array, which is much smaller. This approximation can be used as a preconditioner in solv...
متن کاملTikhonov Regularization in Kronecker Product Approximation for Image Restoration with Mean Boundary Conditions
Truncated Singular Value Decomposition (TSVD) regularization method have been used by Zhao et al. [ " Kronecker product approximations for image restoration with new mean boundary conditions " (2011), Applied Mathematical Modelling, Vol. 36, pp. 225-237]. In this report, I propose an alternative regularization the Tikhonov method. The new regularization method gives better relative error when a...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10024-1