The Dantzig selector and generalized thresholding

The Dantzig selector is a recently introduced technique for near-optimal estimation of sparse signals from a limited set of measurements. This paper offers an interpretation of the Dantzig selector as a generalized thresholding operator. This interpretation ties together two seemingly disparate phenomena: the fact that we can estimate sparse signal accurately, and the fact that we can compute this estimation efficiently using a homotopy algorithm.