Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with $\ell_1$-regularization: \min \|x\|_1 + \bar{\mu} f(x). We investigate the application of this algorithm to compressed sensing signal recovery, in which $f(x) = \frac{1}{2}\|Ax-b\|_M^2$, $A \in \R^{m \times n}$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1007}, url = {http://global-sci.org/intro/article_detail/jcm/8514.html} }