Fuzzy singular value shrinkage for Poisson image denoising

Poisson noise is a fundamental problem in various imaging applications, such as low-light photography, computed tomography and fluorescence microscopy. To remove Poisson noise, an adaptive iterative singular value shrinkage algorithm based on variance-stabilizing transformation (VST) and fuzzy logic classification is proposed in this paper. Since Poisson noise is signal dependent, we use the VST to convert it into signal independent Gaussian noise. The transformed image is divided into a number of blocks, and the similarity of these blocks is well judged according to the similarity criterion of an approximate Kullback–Leibler (KL) distance, and they are arranged to form a low-rank matrix. Then, the proposed algorithm uses singular value decomposition and adaptive soft-thresholding contraction operator to reduce noise, because large singular values point to the position of interesting information, and small singular values point to the position of the noise. In addition, to better preserve the structural information of the image, an adaptive iterative regularization technique based on fuzzy logic classification is proposed. Finally, a potentially noise-free image is obtained by unbiased inverse VST. Experimental results show that the proposed algorithm is competitive with several popular Poisson denoising techniques in both visual and objective metrics.