Compressed sensing and r-algorithms

This paper concerns the author's research in progress. It is not a paper of a completed work. We have a principal example, nuclear norm optimization problem, which is described intuitively and formally. We believe that the proper formulation (and implementation) of r-algorithm based solution of the problem will have general applications and we are still seeking that formulation (and implementation). It lies somewhere in the neighborhood of a matrix extension of r-algorithms. In the framework we consider approaches and problems of compressed sensing, review new results in the field and investigate applications of r-algorithms and their modifications to solution of the problem recovering the data matrix from a sampling of its elements.