Soft Homotopy via Moore-Penrose Inverse

The acquisition of a discrete-time signal is an im-portant 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 T) -1 and the matrix multiplication $A$ T (AA T) -1 can be done before the iteration starts, where $^{\top}$ is the transpose. Numerical examples illustrate the improved error performance for different values of the shrinking parameter $\gamma$. It is found that the greater the shrinking parameter, the less the signal recovery error one could obtain from the two new approaches.