The Research On Gradient Pursuit Algorithms For Compressed Sensing

The theory of Compressed Sensing(CS) can accurately or approximately reconstruct the original signal only with a small amount of samples. Reconstruction a lgorithms of CS directly affect the reconstructed accuracy of signals. The paper focuses on the gradient pursuit algorithms with main innovations as follows:(1) The paper puts forward a variable metric method based gradient pursuit(VMMGP) algorithm. VMMGP uses the idea of variable metric method solving unconstrained optimization problem instead of traditional greedy iterative algorithm for calculation the inverse matrix or generalized inverse matrix, which greatly reduces the computational complexity and storage requirements during each iteration. The convergence of VMMGP is also present. Experimental results show VMMGP algorithm reduces the computational complexity and has the best reconstruction effect among all the gradient pursuit algorithms in the paper, both for one-dimensional speech signal or two-dimensional image signal.(2) The paper proposes a hard thresholding based gradient pursuit algorithm which uses the atom selection strategy of iterative hard thresholding algorithm into gradient pursuit algorithms, so that the proposed algorithms choose atoms more precisely and rapidly. Different hard thresholding based gradient pursuit algorithms can be formed with different gradient directions. The convergence of this algorithm is also present. Experimental results show the reconstruction effect of the proposed algorithms is better than their corresponding gradient pursuit algorithms.(3) The paper gives a variable metric method gradient pursuit based KSVD(VMMGP-KSVD) for hard thresholding gradient pursuit algorithm. The algorithm firstly presents a VMMGP-KSVD dictionary learning method which uses VMMGP as the greedy iterative algorithm in KSVD to calculate coefficient matrix. After sparsing the signal by trained dictionary, the proposed algorithm uses hard thresholding based gradient pursuit algorithms to reconstruct signals. Experimental results show that the reconstruction effect of the proposed algorithms is superior to their corresponding hard thresholding based gradient pursuit algorithms.