KRONECKER PRODUCT AND SVD APPROXIMATIONS IN IMAGE-RESTORATION

Image restoration applications often result in iii-posed least squares problems involving large, structured matrices. One approach used exte nsively is to restore the image in the frequency domain, thus providin g fast algorithms using fast Fourier transforms (FFTs). This is equiva lent to using a circulant approximation to a given matrix. Iterative m ethods may also be used effectively by exploiting the structure of the matrix. While iterative schemes are more expensive than FFT-based met hods, it has been demonstrated that they are capable of providing bett er restorations. As an alternative, we propose an approximate singular value decomposition (SVD), which can be used in a variety of applicat ions. Used as a direct method, the computed restorations are comparabl e to iterative methods but are computationally less expensive. In addi tion, the approximate SVD may be used with the generalized cross valid ation method to choose regularization parameters. It is also demonstra ted that the approximate SVD can be an effective preconditioner for it erative methods. (C) 1998 Elsevier Science Inc. All rights reserved.