An alternating semiproximal method for nonconvex regularized structured total least squares problems

We consider a broad class of regularized stru ctured total least squares (RSTLS) problems encompassing many scenarios in image processing. This class of problems results in a nonconvex and often nonsmooth model in large dimension. To tackle this difficult class of problems we introduce a novel algorithm which blends proximal and alternating minimization methods by beneficially exploiting data information and structures inherently present in RSTLS. The proposed algorithm, which can also be applied to more general problems, is proven to globally converge to critical points and is amenable to efficient and simple computational steps. We illustrate our theoretical findings by presenting numerical experiments on deblurring large scale images, which demonstrate the viability and effectiveness of the proposed method.