Structured Total Least Squares for Color Image Restoration

The problem of 3 x 3 color mixing image restoration is considered. The blurring matrices, as well as the observed image, are contaminated by noise; therefore the total least squares (TLS) method is employed to restore the original image. Since the blurring matrices are also structured, we apply the structured total least squares (STLS) method [J. B. Rosen, H. Park, and J. Glick, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 110-126]. The blurring matrices are generally ill conditioned; thus Tikhonov's regularization is used to stabilize the solution. Since Neumann boundary conditions are used in the restoration process, the discrete cosine transform (DCT) based preconditioner is effective for the linear systems encountered in our STLS algorithm.