Channel Interaction Graph Laplacian Regularizer for Blind Color Image Deblurring

Blind color image deblurring constitutes a highly ill-posed inverse problem, for which the design of effective image priors is essential. Although exploiting inter-channel correlations is critical to maintaining color consistency, most existing low-rank priors depend on computationally expensive explicit tensor decompositions. To address this limitation, we introduce a Channel Interaction Graph Laplacian Regularizer, which implicitly promotes a low-rank configuration of the gradient covariance matrix through a trace-based formulation, thereby preserving cross-channel structural coherence without resorting to singular value decomposition. When combined with an \(\ell _0\) ${\ell }_0$ gradient sparsity prior and a kernel energy constraint, the resulting variational model enables the joint estimation of a sharp latent image and a reliable blur kernel. Experimental results on both synthetic and real-world datasets indicate that the proposed approach consistently produces sharper visual reconstructions with reduced artifacts, while surpassing state-of-the-art methods in terms of visual quality and quantitative performance.