Alternating block coordinate proximal forward-backward descent for nonconvex regularised problems with biconvex terms

In this work we consider a broad class of smooth optimization problems composed of a biconvex data-fidelity terms and smooth, nonconvex regularisation terms. We propose a family of attractive schemes for solving this class of problems. It is based on the standard alternate proximal linearized forward-backward approach. Unlike the existing prox-based algorithms, our approach exploits the biconvex structure of the data term. Thus we use proximity operators with respect to convex functions only. The iterates are uniquely defined, independently of the form of regularization terms.