Projective iterative hard thresholding algorithm for sparse signal recovery

Recovering sparse signals from a few linear measurements is attracting growing attention. Bsides sparsity, the signals usually are nonnegative, nonpositive or restricted in some domain. This paper proposes an algorithm for recovering the sparse signal with some certain property on learning the sparsity. We propose this algorithm by combining the projective method with the iterative hard thresholding strategy. We prove that this algorithm is linear convergent provided the sensing matrix has suitable property. Numerical results demonstrate the efficiency of the algorithm.