Fast Cadzow’s Algorithm and a Gradient Variant

Abstract

The Cadzow’s algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast Cadzow’s algorithm which is developed by incorporating a novel subspace projection to reduce the high computational cost of the SVD in the Cadzow’s algorithm. Then a Gradient method and a Fast Gradient method are proposed to address the non-decreasing MSE issue when applying the Cadzow’s or Fast Cadzow’s algorithm for signal denoising. Extensive empirical performance comparisons demonstrate that the proposed algorithms can complete the denoising and recovery tasks more efficiently and effectively.