We present a method for image denoising based on singular value shrinkage that fuses soft and hard thresholds. The technique simply groups similar patches from a noisy image as low-rank matrices and shrinks the singular values by the combination of soft and hard thresholds. On one hand, a hard threshold approximation method based on nonlocal self-similarity and low-rank approximation is used for fast selection of hard threshold; on the other hand, a soft threshold selection method based on random matrix and asymptotic matrix reconstruction theory is designed. In addition, we also propose an adaptive backward projection algorithm based on image phase congruency and gradient calculation so that the input images participating in the iteration are adaptive. This method improves the traditional fixed coefficient backward projection method and makes the robustness of the algorithm better. The experimental results of denoising and enhancement for a number of natural images show that the proposed algorithms have significant improvement in both subjective visual effect and objective quantization index by comparing with some related state-of-the-art denoising algorithms.
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