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Non-uniform blind deblurring for general dynamic scenes is a challenging computer vision problem as blurs arise not only from multiple object motions but also from camera shake, scene depth variation. To remove these complicated motion…

Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…

This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…

Search and retrieval remains a major research topic in several domains, including computer graphics, computer vision, engineering design, etc. A search engine requires primarily an input search query and a database of items to search from.…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

In recent years extensions of manifold Ricci curvature to discrete combinatorial objects such as graphs and hypergraphs (popularly called as "network shapes"), have found a plethora of applications in a wide spectrum of research areas…

Motivated by optimization with differential equations, we consider optimization problems with Hilbert spaces as decision spaces. As a consequence of their infinite dimensionality, the numerical solution necessitates finite dimensional…

Recent methods for boundary or edge detection built on Deep Convolutional Neural Networks (CNNs) typically suffer from the issue of predicted edges being thick and need post-processing to obtain crisp boundaries. Highly imbalanced…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

Fault-tolerant deep learning accelerator is the basis for highly reliable deep learning processing and critical to deploy deep learning in safety-critical applications such as avionics and robotics. Since deep learning is known to be…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a…

We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i.e., loss landscape of an NN contains all critical points of all the narrower NNs.…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation,…

The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…

In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…

This work investigates how using reduced precision data in Convolutional Neural Networks (CNNs) affects network accuracy during classification. More specifically, this study considers networks where each layer may use different precision…

A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…