Bregman iterative algorithms for compressed sensing

Stanley Osher
University of California, Los Angeles (UCLA)

Bregman iterative regularization (1967) was introduced by Osher, Burger, Goldfarb, Xu and Yin as a device for improving TV based image restoration (2004) and was used by Xu and Osher in (2006) to analyze and improve wavelet shrinkage. In recent work by Yin, Osher, Goldfarb and Darbon we devised simple and extremely efficient methods for solving the basis pursuit problem which is used in compressed sensing.
A linearized version of Bregman iteration was also done by Osher, Dong, Mao and Yin. This requires two lines of MATLAB code and is remarkably efficient. This means we rapidly and easily solve the problem:
minimize the L1 norm of u so that Au=f
for a given k by n matrix A, with k<

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