Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD is ill-posed. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and yield the unique solution. However, existing theoretical analysis on uniqueness in BD is rather limited. In an earlier paper of ours [1], we provided the first algebraic sample...

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. Thereis now a rich class of structured sparsity approaches that expand the modeling power of the sparsityparadigm and incorporate constraints such as group sparsity, graph sparsity, or hierarchical sparsity. Whilethese sparsity models offer improved sample complexity and better interpr...

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the `1-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections on...