A regularized structured total least squares algorithm for high-resolution image reconstruction

High-resolution image reconstruction is an important problem in image processing. In general, the blurring matrices are ill-conditioned, and it is necessary to compute a regularized solution. Moreover, error exists not only in the blurred image but also the blurring matrix, thus the total least squares method tends to give better results than the ordinary least squares method. Since the blurring matrices are also structured, it is more appropriate to apply Structured Total Least Squares (STLS). Ng et al. [Int. J. Imaging Systems Technol. 12 (2002) 35] recently proposed a Regularized Constrained Total Least Squares (RCTLS) algorithm for this problem. RCTLS is essentially a different name for Regularized Structured Total Least Squares (RSTLS). However, Ng et al. solved a problem that approximates the RCTLS problem. The algorithm proposed in this paper solves the exact regularization of the STLS problem, and it is a faster algorithm. Also proposed is a preconditioner for the linear systems encountered in our RSTLS algorithm.