Fast reconstruction with barrier projection for compressively sensed image array

Abstract

This paper considers an improved log-barrier algorithm for the signal recovery from compressively sensed image arrays. The improvements include the barrier projection algorithm, the implementation of parallel computation, the conjugate direction method, and the estimation of Hessian matrix inversion in Newton steps. The number of inner and outer iterations are reduced by appropriate space transformation eliminating linear and second-order barriers. Considering a problem of scale N with l and L being the number of log-barrier and Newton steps, the complexity of original log-barrier algorithm, which is O(N2lL), can be reduced to O(N2L) or O(NlL).