Convolutional dual graph Laplacian sparse coding

Xuefeng Peng, Fei Chen, Hang Cheng, Meiqing Wang

In recent years, graph signal processing (GSP) technology has become popular in various fields, and graph Laplacian regularizers have also been introduced into convolutional sparse representation. This paper proposes a convolutional sparse representation model based on the dual graph Laplacian regularizer to ensure effective application of a dual graph signal smoothing prior on the rows and columns of input images.The graph Laplacian matrix contains the gradient information of the image and the similarity information between pixels, and can also describe the degree of change of the graph, so the image can be smoothed. Compared with the single graph smoothing prior, the dual graph has a simple structure, relaxes the conditions, and is more conducive to image restoration using the image signal prior. In this paper, this paper formulated the corresponding minimization problem using the proposed model, and subsequently used the alternating direction method of multiplication (ADMM) algorithm to solve it in the Fourier domain.Finally, using random Gaussian white noise for the denoising experiments. Compared with the single graph smoothing prior,the denoising results of the model with dual graph smoothing prior proposed in this paper has fewer noise points and clearer texture.

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