This paper presents a variant of the iterative shrinkage-thresholding (IST) algorithm,\ncalled backtracking-based adaptive IST (BAIST), for image compressive sensing (CS) reconstruction.\nFor increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity.\nTo add back more details, the BAIST method backtracks to the previous noisy image using L2 norm\nminimization, i.e., minimizing the Euclidean distance between the current solution and the previous\nones. Through this modification, the BAIST method achieves superior performance while maintaining\nthe low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive\nregularizor to automatically detect the sparsity level of an image. Experimental results show that our\nalgorithm outperforms the original IST method and several excellent CS techniques.
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