Algorithm-Induced Prior for Image Restoration
This work addresses a theoretical gap for researchers in computational imaging by providing a clearer understanding of implicit priors, though it is incremental as it builds on existing ADMM frameworks.
The paper tackled the challenge of analyzing algorithm-induced priors in image restoration by deriving an explicit expression for the prior induced by the ADMM algorithm using symmetric smoothing filters, resulting in stronger reconstruction performance compared to conventional graph Laplacian methods, with validation through image inpainting experiments.
This paper studies a type of image priors that are constructed implicitly through the alternating direction method of multiplier (ADMM) algorithm, called the algorithm-induced prior. Different from classical image priors which are defined before running the reconstruction algorithm, algorithm-induced priors are defined by the denoising procedure used to replace one of the two modules in the ADMM algorithm. Since such prior is not explicitly defined, analyzing the performance has been difficult in the past. Focusing on the class of symmetric smoothing filters, this paper presents an explicit expression of the prior induced by the ADMM algorithm. The new prior is reminiscent to the conventional graph Laplacian but with stronger reconstruction performance. It can also be shown that the overall reconstruction has an efficient closed-form implementation if the associated symmetric smoothing filter is low rank. The results are validated with experiments on image inpainting.