A relaxed iterative thresholding reconstruction algorithm based on compressed sensing

Abstract

Based on the iterative hard thresholding (IHT) algorithm, this paper presents the relaxed iterative thresholding algorithm which is a modified algorithm of the conventional IHT algorithm. By introducing the relaxed factors, modifying the iterative formulae and proposing the relaxed algorithm correspondingly, we acquired the least number of iterations and error estimate required by the measurement matrices of satisfying the RIP. Compared with the IHT algorithm, the method presented in this paper not only has the advantages of keeping linear stability and clearly delimiting the upper limit of the number of iterations, but also obtains the same computational precision with the less number of iterations which saves the labor of calculation. Finally, taking the Hadamard orthogonal basis as sparse basis, the random Gaussian matrix as measurement matrix, we have verified the validity of the algorithm proposed above by experimental simulation. © Springer-Verlag Berlin Heidelberg 2012.