A Generalized Hard Thresholding Pursuit on Infinite Unions of Subspaces

Abstract:
Hard thresholding pursuit (HTP) has been introduced to the field of compressive sensing as an algorithm to solve underdetermined linear systems of equations where the solution is assumed to be a sparse vector. This sparsity constraint of the solution can be expressed in terms of a finite union of particular subspaces. The present paper shows how HTP can be generalized to linear inverse problems with solutions in an arbitrary (infinite) union of subspaces. We incorporate the idea of inexact projections. This allows for more flexibility in calculating a crucial step of the generalized HTP, which is beneficial in practical considerations. We show how the HTP algorithm can be used in conjunction with Root MUSIC for channel estimation in millimeter-wave communication systems.