Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising

摘要

We propose and analyze an extremely fast, efficient and simple method. This method was first described with more details and rigorous theory given. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, Donoho, et.al. Our method introduces an improvement called 'kicking' of the very efficient method and also applies it to the problem of denoising of undersampled signals. The use of Bregman iteration for denoising of images began and led to improved results for total variation based methods. Here we apply it to denoise signals, especially essentially sparse signals, which might even be undersampled.