Soft Thresholding Using Moore–Penrose Inverse

The acquisition of a discrete-time signal is an important part of a compressive sensing problem. A high-accuracy algorithm that could bring better signal recovery performance is often called for. In this work, two thresholding algorithms that involve a soft thresholding decision are proposed using the Moore–Penrose inverse. Numerical examples are conducted and illustrate that, in the optimal case, both proposed methods consume the computational time at the same level as the conventional soft homotopy algorithm (SHA). Under no knowledge of the optimal regularization parameter, both methods will perform better than the conventional SHA with less amount of required time for the computation. Taking the nonsparse electroencephalogram signal from a real measurement into account, all soft thresholding algorithms provide nearly the same error performance for several compression ratios, while the proposed methods consume less computational time than the conventional SHA.