Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising

We propose and analyze an extremely fast, efficient and simple method for solving the problem: min{ u 1 :Au=f,u∈Rn }. This method was first described in [1], with more details in [2] and rigorous theory given in [3] and [4]. The motivation was compressive sensing, which now has a vast and exciting history, which seems to have started with Candes, et.al. [5] and Donoho, [6]. See [2], [3] and [4] for a large set of references. Our method introduces an improvement called “kicking” of the very efficient method of [1], [2] and also applies it to the problem of denoising of undersampled signals. The use of Bregman iteration for denoising of images began in [7] 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. Key words. 1-minimization, basis pursuit, compressed sensing, sparse denoising, iterative regularization subject classifications. 49, 90, 65

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Stanley Osher, Yu Mao, Bin Dong, Wotao Yin
• Keywords: CORR 2011, Denoising, Education, Iterative Regularization Subject, Variation Based Methods