Abstract:In recent years, deep learning-based methods have shown excellent performance in the field of image restoration. However, most deep networks are structured based on experience, and less consideration is given to fusion with existing traditional algorithms, therefore these networks arepoorly interpretable. To address this problem, an image restoration algorithm based on wavelet domain ADMM deep networkwasproposed. Firstly, a wavelet transform is introduced to the data term as well as the prior term simultaneously, an image recovery model under wavelet domain was proposed. Consequently the image recovery problem was transformed from spatial domain into wavelet domain, and a new image degradation model and recovery cost function were constructed. Then, in order to effectively reduce the difficulty of the optimal solution, the ADMM algorithm was introduced to further decompose it into a more manageable restoration subproblem and a denoising subproblem, and obtain the best estimate of the wavelet domain image through continuous optimization. Finally, the specific form of the solution based on the above optimization process guides the construction of a deep convolutional neural network to achieve end-to-end image recovery. The perceptual field and spatial feature mappingsizeof this networkis increased and decreased respectivelysince the image processing was executed in the wavelet domain. Not only does it achieve better performance, but also significantly reduces the complexity of operations and increases the processing speed. The proposed network was applied to image deblurring and image denoising tasks to verify the recovery performance on Set10, BSD68 and Urban100 datasets. The relevant experimental results show that the proposed algorithm achieves better recovery results for both deblurring and denoising tasks, with an increase of 0.08~0.18 dB in PSNR values while the resultant images retain more detailed information, thus outperforming the comparison methods in both quantitative and qualitative results.