A Residual Solver and Its Unfolding Neural Network for Total Variation Regularized Models
This work addresses image processing problems for researchers and practitioners, offering an incremental improvement with a new algorithm and neural network for total variation models.
The paper tackles solving Total Variation regularized models by introducing a Residual Solver algorithm that finds the residual between input and optimal solution, proven to reach the same global optimal solutions as classical methods on 500 natural images, and unfolds it into an unsupervised convolutional neural network for applications like image smoothing and denoising.
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.