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Fixed-point continuation applied to compressed sensing: Implementation and numerical experiments. (English) Zbl 1224.65153
Summary: We investigate the application of this algorithm to compressed sensing signal recovery, in which $$f(x)=\frac12 \|Ax-b\|^2_M$$, $$A\in \mathbb R^{m\times n}$$, and $$m\leq n$$. In particular, we extend the original algorithm to obtain better practical results, derive appropriate choices for $$M$$ and $$\bar{\mu}$$ under a given measurement model, and present numerical results for a variety of compressed sensing problems. The numerical results show that the performance of our algorithm compares favorably with that of several recently proposed algorithms.

##### MSC:
 65K05 Numerical mathematical programming methods 90C06 Large-scale problems in mathematical programming 90C90 Applications of mathematical programming 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 90C20 Quadratic programming
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