Chapter 5

Stability of Linear Sparse Optimization Methods

The presence of noise in data is an unavoidable issue due to sensor imperfection, estimation inaccuracy, statistical or communication errors. For instance, signals might be contaminated by some form of random noise and the measurements of signals are subject to quantization error. Thus a huge effort is made in sparse data recovery, to ensure that the recovery method is stable in the sense that recovery errors stay under control when the measurements are slightly inaccurate and when the data is not exactly sparse [37, 95, 97, 108]. The stability of many recovery algorithms, including 1-minimization, has been extensively studied under various assumptions such as the RIP, NSP and mutual ...

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