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CORR
2011
Springer

Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising

11 years 3 months ago
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
Stanley Osher, Yu Mao, Bin Dong, Wotao Yin
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Stanley Osher, Yu Mao, Bin Dong, Wotao Yin
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