Related papers: Least-Squares Neural Network (LSNN) Method For Lin…

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…

It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…

Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or…

In deformable registration, the geometric framework - large deformation diffeomorphic metric mapping or LDDMM, in short - has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. Grounded in…

The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online…

For solving a wide class of nonconvex and nonsmooth problems, we propose a proximal linearized iteratively reweighted least squares (PL-IRLS) algorithm. We first approximate the original problem by smoothing methods, and second write the…

In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based…

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…

Most existing Convolutional Neural Networks(CNNs) used for action recognition are either difficult to optimize or underuse crucial temporal information. Inspired by the fact that the recurrent model consistently makes breakthroughs in the…

The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales,…

Constrained least-squares regression problems, such as the Nonnegative Least Squares (NNLS) problem, where the variables are restricted to take only nonnegative values, often arise in applications. Motivated by the recent development of the…

Porting state of the art deep learning algorithms to resource constrained compute platforms (e.g. VR, AR, wearables) is extremely challenging. We propose a fast, compact, and accurate model for convolutional neural networks that enables…

Many classic methods have shown non-local self-similarity in natural images to be an effective prior for image restoration. However, it remains unclear and challenging to make use of this intrinsic property via deep networks. In this paper,…

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs). Such models, widely used in the random feature method…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…

Neural networks are usually trained with different variants of gradient descent based optimization algorithms such as stochastic gradient descent or the Adam optimizer. Recent theoretical work states that the critical points (where the…

Deep neural networks have demonstrated highly competitive performance in super-resolution (SR) for natural images by learning mappings from low-resolution (LR) to high-resolution (HR) images. However, hyperspectral super-resolution remains…