Soft Homotopy through Moore-Penrose Inverse

Abstract

The acquisition of a discrete-time signal is an important part of a compressive sensing problem. A fine algorithm that could bring better signal recovery performance is often called for. In this work, two homotopy algorithms that involve a soft thresholding decision are proposed using the Moore-Penrose inverse. The additional complexity required in the two proposed methods is relatively minimal, since the necessary matrix inverse (AA⊺)-1 and the matrix multiplication A⊺(AA⊺)-1 can be done before the iteration starts, where ·⊺ is the transpose. Numerical examples illustrate the improved error performance for different values of the shrinking parameter γ. It is found that the greater the shrinking parameter, the less the signal recovery error one could obtain from the two new approaches. © 2022 IEEE.