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We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

Deep learning algorithms have demonstrated state-of-the-art performance in various tasks of image restoration. This was made possible through the ability of CNNs to learn from large exemplar sets. However, the latter becomes an issue for…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

The design of metamaterials which support unique optical responses is the basis for most thin-film nanophotonics applications. In practice this inverse design problem can be difficult to solve systematically due to the large design…

Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this…

Deep learning has become very popular for tasks such as predictive modeling and pattern recognition in handling big data. Deep learning is a powerful machine learning method that extracts lower level features and feeds them forward for the…

Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms.…

Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…

Variational method and deep learning method are two mainstream powerful approaches to solve inverse problems in computer vision. To take advantages of advanced optimization algorithms and powerful representation ability of deep neural…

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…

Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly…

While deeper and wider neural networks are actively pushing the performance limits of various computer vision and machine learning tasks, they often require large sets of labeled data for effective training and suffer from extremely high…

Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…

We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with…

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…

The image reconstruction process in medical imaging can be treated as solving an inverse problem. The inverse problem is usually solved using time-consuming iterative algorithms with sparsity or other constraints. Recently, deep neural…

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

This paper proposes a novel approach to regularize the ill-posed blind image deconvolution (blind image deblurring) problem using deep generative networks. We employ two separate deep generative models - one trained to produce sharp images…