A POCS-based constrained total least squares algorithm for image restoration

In image restoration, the region of support of the point spread function is often much smaller than the size of the observed degraded image and this property is utilized in many image deconvolution algorithms. For the constrained total least squares (CTLS)-based algorithm, it means that the solution of the CTLS algorithm should retain the block-circulant and sparse structure of the degradation matrix simultaneously. In real image restoration problems, the CTLS method often involves large-scale computation and is often solved using Mesarovic et al.’s algorithm. However, there is concern about whether their algorithm preserves the sparse structure of the degradation matrix. In this paper, we prove that by imposing an extra constraint, the sparse structure in their algorithm can be preserved. Then, we use the projection onto convex sets algorithm to find a solution to this extended formulation. Our experimental study indicates that the proposed method performs competitively, and often better, in terms of visual and objective evaluations.