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The great success of Deep Neural Networks (DNNs) has inspired the algorithmicdevelopment of DNN-based Fixed-Point (DNN-FP) for computer vision tasks. DNN-FPmethods, trained by Back-Propagation Through Time or computing the inaccurateinversion of the Jacobian, suffer from inferior representation ability.Motivated by the representation power of the Transformer, we propose aframework to unroll the FP and approximate each unrolled process viaTransformer blocks, called FPformer. To reduce the high consumption of memoryand computation, we come up with FPRformer by sharing parameters between thesuccessive blocks. We further design a module to adapt Anderson acceleration toFPRformer to enlarge the unrolled iterations and improve the performance,called FPAformer. In order to fully exploit the capability of the Transformer,we apply the proposed model to image restoration, using self-supervisedpre-training and supervised fine-tuning. 161 tasks from 4 categories of imagerestoration problems are used in the pre-training phase. Hereafter, thepre-trained FPformer, FPRformer, and FPAformer are further fine-tuned for thecomparison scenarios. Using self-supervised pre-training and supervisedfine-tuning, the proposed FPformer, FPRformer, and FPAformer achievecompetitive performance with state-of-the-art image restoration methods andbetter training efficiency. FPAformer employs only 29.82% parameters used inSwinIR models, and provides superior performance after fine-tuning. To trainthese comparison models, it takes only 26.9% time used for training SwinIRmodels. It provides a promising way to introduce the Transformer in low-levelvision tasks.

Towards Vision Transformer Unrolling Fixed-Point Algorithm: a Case Study on Image Restoration