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In this paper, we propose a novel algorithm for analysis-based sparsityreconstruction. It can solve the generalized problem by structured sparsityregularization with an orthogonal basis and total variation regularization. Theproposed algorithm is based on the iterative reweighted least squares (IRLS)model, which is further accelerated by the preconditioned conjugate gradientmethod. The convergence rate of the proposed algorithm is almost the same asthat of the traditional IRLS algorithms, that is, exponentially fast. Moreover,with the specifically devised preconditioner, the computational cost for eachiteration is significantly less than that of traditional IRLS algorithms, whichenables our approach to handle large scale problems. In addition to the fastconvergence, it is straightforward to apply our method to standard sparsity,group sparsity, overlapping group sparsity and TV based problems. Experimentsare conducted on a practical application: compressive sensing magneticresonance imaging. Extensive results demonstrate that the proposed algorithmachieves superior performance over 14 state-of-the-art algorithms in terms ofboth accuracy and computational cost.

Fast Iteratively Reweighted Least Squares Algorithms for Analysis-Based Sparsity Reconstruction