New dual method for elastica regularization.

The Euler's elastica energy regularizer has been widely used in image processing and computer vision tasks. However, finding a fast and simple solver for the term remains challenging. In this paper, we propose a new dual method to simplify the solution. Classical fast solutions transform the complex optimization problem into simpler subproblems, but introduce many parameters and split operators in the process. Hence, we propose a new dual algorithm to maintain the constraint exactly, while using only one dual parameter to transform the problem into its alternate optimization form. The proposed dual method can be easily applied to level-set-based segmentation models that contain the Euler's elastic term. Lastly, we demonstrate the performance of the proposed method on both synthetic and real images in tasks image processing tasks, i.e. denoising, inpainting, and segmentation, as well as compare to the Augmented Lagrangian method (ALM) on the aforementioned tasks.

Iterative deep neural networks based on proximal gradient descent for image restoration.

The algorithm unfolding networks with explainability of algorithms and higher efficiency of Deep Neural Networks (DNN) have received considerable attention in solving ill-posed inverse problems. Under the algorithm unfolding network framework, we propose a novel end-to-end iterative deep neural network and its fast network for image restoration. The first one is designed making use of proximal gradient descent algorithm of variational models, which consists of denoiser and reconstruction sub-networks. The second one is its accelerated version with momentum factors. For sub-network of denoiser, we embed the Convolutional Block Attention Module (CBAM) in previous U-Net for adaptive feature refinement. Experiments on image denoising and deblurring demonstrate that competitive performances in quality and efficiency are gained by compared with several state-of-the-art networks for image restoration. Proposed unfolding DNN can be easily extended to solve other similar image restoration tasks, such as image super-resolution, image demosaicking, etc.