  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.
