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. In the final version,
we will show how the HTP algorithm can be used in conjunction
with Root MUSIC for channel estimation in millimeter wave
communication systems.