Adaptively regularized constrained total least-squares image restoration

In this paper, a novel algorithm for image restoration is proposed based on constrained total least-squares (CTLS) estimation, that is, adaptively regularized CTLS (ARCTLS). It is well known that in the regularized CTLS (RCTLS) method, selecting a proper regularization parameter is very difficult. For solving this problem, we take the first-order partial derivative of the classic equation of RCTLS image restoration and do some simplification with it. Then, we deduce an approximate formula, which can be used to adaptively calculate the best regularization parameter along with the degraded image to be restored. We proved that the convergence and the stability of the solution could be well satisfied. The results of our experiments indicate that using this method can make an arbitrary initial parameter be an optimal one, which results in a good restored image of high quality.