## Matlab codes for linearized Bregman algorithmsWotao Yin## Sparse signal recoveryThe linearized Bregman algorithms return the solution to by solving the model with an appropriate . ## Choice ofExact regularization problem: for any and , there exists so that any “equalizes” the two problems, namely, as if does not exist. Proofs can be found in this paper and this paper. depends on the data, but a typical value is 1 to 10 times the estimate of . This choice is justified in this paper. ## What if ?If does not hold (as is noisy or is approximately sparse, or both), one can stop the algorithms when and obtain as a sparse solution. Like most other dual algorithms, the intermediate iterates are sparse. ## Matlab codes and demosComparisons: binary sparse test 1 test 2; Gaussian sparse test 1 test 2; Bernoulli matrix test 1 test 2; partial DCT matrix test 1 test 2
## Low-rank matrix recovery / matrix completionThe linearized Bregman algorithms return the solution to by solving the model where does the matrix nuclear-norm. ## Choice ofA typical value is 1 to 10 times the estimate of , the spectral norm of . This choice is justified in this paper. ## Matrix completion Matlab demosAlgorithms: fixed stepsize version, line search version, Nesterov acceleration with reset Examples: easy, difficult 1, difficult 2
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