Quaternion-based Deep Image Prior with Regularization by Denoising for Color Image Restoration

Deep image prior (DIP) has demonstrated remarkable efficacy in addressing various imaging inverse problems by capitalizing on the inherent biases of deep convolutional architectures to implicitly regularize the solutions. However, its application to color images has been hampered by the conventional DIP method's treatment of color channels in isolation, ignoring their important inter-channel correlations. To mitigate this limitation, we extend the DIP framework from the real domain to the quaternion domain and propose a novel quaternion deep image prior (QDIP) model for color image restoration. More importantly, to enhance the recovery performance of QDIP and alleviate its susceptibility to the unfavorable overfitting issue, we propose incorporating the concept of regularization by denoising (RED). This approach leverages existing denoisers to regularize inverse problems and integrates the RED scheme into our QDIP model. Extensive experiments on color image denoising, deblurring, and super-resolution show that the proposed QDIP and QDIP-RED achieve highly competitive performance against many state-of-the-art alternatives in both quantitative and qualitative evaluations. The dataset and code can be available at: https://github.com/qiuxuanzhizi/QDIP-RED