Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments

Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with ₁-regularization: We investigate the application of this algorithm to compressed sensing signal recovery, in which f(x) = 1/2\|Ax-b\|M², A ∈ Rm × n and m ≤ n. In particular, we extend the original algorithm to obtain better practical results, derive appropriate choices for M and μ̄ 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.