Denoising with greedy-like pursuit algorithms

This paper provides theoretical guarantees for denoising performance of greedy-like methods. Those include Compressive Sampling Matching Pursuit (CoSaMP), Subspace Pursuit (SP), and Iterative Hard Thresholding (IHT). Our results show that the denoising obtained with these algorithms is a constant and a log-factor away from the oracle´s performance, if the signal´s representation is sufficiently sparse. Turning to practice, we show how to convert these algorithms to work without knowing the target cardinality, and instead constrain the solution to an error-budget. Denoising tests on synthetic data and image patches show the potential in this stagewise technique as a replacement of the classical OMP.