Abstract: Aiming at the problem that the current sparse denoising algorithm has low decomposition efficiency and unsatisfactory denoising effect,an image denoising algorithm based on adaptive matching pursuit was proposed.Firstly,the algorithm uses the adaptive matching pursuit algorithm to solve the sparse coefficients,and then uses the K-means singular value decomposition algorithm to train the dictionary into an adaptive dictionary that can effectively reflect the image structure features.Finally,theima-ge is reconstructed by combining the sparse coefficient with the adaptive dictionary.During the reconstruction process,the coefficients corresponding to the noise are removed,and finally the denoising effect is achieved.Spike-Slab priori is introduced to guide the sparsity of sparse coefficient matrix,and two weight matrices are used to make the denoising model more realistic.In view of the importance of dictionary in sparse algorithm,this paper compared adaptive dictionary with DCT redundant dictionary and Global dictionary.The experimental results show that the denoising result of adaptive dictionary is about 4.5 dB higher than that of traditional dictionary in terms of peak signal-to-noise ratio (PSNR).The proposed method improves three evaluation indicators in varying degrees compared with the current six main methods of sparse denoising.The PSNR is increased by about 0.76dB to 6.24 dB,the feature similarity (FSIM) is increased by about 0.012 to 0.082,and the structure similarity (SSIM) is increased by about 0.015 to 0.108 on average.The qualitative evaluation of the image denoising algorithm shows that the proposed algorithm retains more useful information and has the best visual effect.Therefore,the experiment fully proves its effectiveness and robustness.

Key words: Adaptive matching pursuit, Image denoising, K-means singular value decomposition, Sparse representation, Spike-Slab priori