An Alternative Thresholding Rule for Compressed Sensing

Compressed Sensing algorithms often make use of the hard thresholding operator to pass from dense vectors to their best s-sparse approximations. However, the output of the hard thresholding operator does not depend on any information from a particular problem instance. We propose an alternative thresholding rule, Look Ahead Thresholding, that does. In this paper we offer both theoretical and experimental justification for the use of this new thresholding rule throughout compressed sensing.