Sparse reconstruction for compressed sensing using Stagewise Polytope Faces Pursuit

Compressed sensing, also known as compressive sampling, is an approach to the measurement of signals which have a sparse representation, that can reduce the number of measurements that are needed to reconstruct the signal. The signal reconstruction part requires efficient methods to perform sparse reconstruction, such as those based on linear programming. In this paper we present a method for sparse reconstruction which is an extension of our earlier polytope faces pursuit algorithm, based on the polytope geometry of the dual linear program. The new algorithm adds several basis vectors at each stage, in a similar way to the recent stagewise orthogonal matching pursuit (StOMP) algorithm. We demonstrate the application of the algorithm to some standard compressed sensing problems.