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Training convolutional neural network models is memory intensive since back-propagation requires storing activations of all intermediate layers. This presents a practical concern when seeking to deploy very deep architectures in production,…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where…

In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or…

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven…

Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation…

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…

The recent successful deep neural networks are largely trained in a supervised manner. It {\it associates} complex patterns of input samples with neurons in the last layer, which form representations of {\it concepts}. In spite of their…

Deep neural networks have gained tremendous popularity in last few years. They have been applied for the task of classification in almost every domain. Despite the success, deep networks can be incredibly slow to train for even moderate…

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

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…

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match…

We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…

An important goal in deep learning is to learn versatile, high-level feature representations of input data. However, standard networks' representations seem to possess shortcomings that, as we illustrate, prevent them from fully realizing…

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…

To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the…