2020/09/08 by Yuanhao Gong, Gong, Yuanhao
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image and Signal Denoising Methods #Image and Video Processing (eess.IV) #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2009.03477
openalex publication_date 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes to solve the Total Variation regularized models by finding the residual between the input and the unknown optimal solution. After analyzing a previous method, we developed a new iterative algorithm, named as Residual Solver, which implicitly solves the model in gradient domain. We theoretically prove the uniqueness of the gradient field in our algorithm. We further numerically confirm that the residual solver can reach the same global optimal solutions as the classical method on 500 natural images. Moreover, we unfold our iterative algorithm into a convolution neural network (named as Residual Solver Network). This network is unsupervised and can be considered as an "enhanced version" of our iterative algorithm. Finally, both the proposed algorithm and neural network are successfully applied on several problems to demonstrate their effectiveness and efficiency, including image smoothing, denoising, and biomedical image reconstruction. The proposed network is general and can be applied to solve other total variation regularized models.