相关论文: An Open Problem on Sparse Representations in Union…

Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the…

Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system…

A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et…

This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by…

In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for representing the approximate. However, this natural choice…

Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…

We present a sparse representation of model uncertainty for Deep Neural Networks (DNNs) where the parameter posterior is approximated with an inverse formulation of the Multivariate Normal Distribution (MND), also known as the information…

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…

We develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (2018), we propose a simple expansion of SD bases so as to…

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…

One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Whereas classical compressed sensing algorithms do…

A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…

Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…

This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…

Many important theorems in combinatorics, such as Szemer\'edi's theorem on arithmetic progressions and the Erd\H{o}s-Stone Theorem in extremal graph theory, can be phrased as statements about independent sets in uniform hypergraphs. In…

In this paper, we have developed an ellipsoid radial basis function neural network (ERBFNN) and algorithm for sparse representing of a molecular shape. To evaluate a sparse representation of the molecular shape model, the Gaussian density…

Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously…