Analysis Plug-and-Play Methods for Imaging Inverse Problems
This is an incremental improvement for researchers in computational imaging, offering an alternative prior formulation without clear broad impact.
The paper tackles imaging inverse problems by proposing an analysis formulation of Plug-and-Play Priors that applies learned priors in the gradient domain instead of the image domain, achieving performance comparable to standard methods in deblurring and super-resolution tasks.
Plug-and-Play Priors (PnP) is a popular framework for solving imaging inverse problems by integrating learned priors in the form of denoisers trained to remove Gaussian noise from images. In standard PnP methods, the denoiser is applied directly in the image domain, serving as an implicit prior on natural images. This paper considers an alternative analysis formulation of PnP, in which the prior is imposed on a transformed representation of the image, such as its gradient. Specifically, we train a Gaussian denoiser to operate in the gradient domain, rather than on the image itself. Conceptually, this is an extension of total variation (TV) regularization to learned TV regularization. To incorporate this gradient-domain prior in image reconstruction algorithms, we develop two analysis PnP algorithms based on half-quadratic splitting (APnP-HQS) and the alternating direction method of multipliers (APnP-ADMM). We evaluate our approach on image deblurring and super-resolution, demonstrating that the analysis formulation achieves performance comparable to image-domain PnP algorithms.