Sparse recovery by semi-iterative hard thresholding algorithm

We propose a computationally simple and efficient method for sparse recovery termed as the semi-iterative hard thresholding (SIHT). Unlike the existing iterative-shrinkage algorithms, which rely crucially on using negative gradient as the search direction, the proposed algorithm uses the linear combination of the current gradient and directions of few previous steps as the search direction. Compared to other iterative shrinkage algorithms, the performances of the proposed method show a clear improvement in iterations and error in noiseless, whilst the computational complexity does not increase.