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The deep unfolding approach has attracted significant attention in computervision tasks, which well connects conventional image processing modelingmanners with more recent deep learning techniques. Specifically, byestablishing a direct correspondence between algorithm operators at eachimplementation step and network modules within each layer, one can rationallyconstruct an almost ``white box'' network architecture with highinterpretability. In this architecture, only the predefined component of theproximal operator, known as a proximal network, needs manual configuration,enabling the network to automatically extract intrinsic image priors in adata-driven manner. In current deep unfolding methods, such a proximal networkis generally designed as a CNN architecture, whose necessity has been proven bya recent theory. That is, CNN structure substantially delivers thetranslational invariant image prior, which is the most universally possessedstructural prior across various types of images. However, standard CNN-basedproximal networks have essential limitations in capturing the rotation symmetryprior, another universal structural prior underlying general images. Thisleaves a large room for further performance improvement in deep unfoldingapproaches. To address this issue, this study makes efforts to suggest ahigh-accuracy rotation equivariant proximal network that effectively embedsrotation symmetry priors into the deep unfolding framework. Especially, wededuce, for the first time, the theoretical equivariant error for such adesigned proximal network with arbitrary layers under arbitrary rotationdegrees. This analysis should be the most refined theoretical conclusion forsuch error evaluation to date and is also indispensable for supporting therationale behind such networks with intrinsic interpretability requirements.

Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration