相关论文: Deterministic construction of sparse binary and te…

High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of…

In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…

We demonstrate that 1x1-convolutions in 1D time-channel separable convolutions may be replaced by constant, sparse random ternary matrices with weights in $\{-1,0,+1\}$. Such layers do not perform any multiplications and do not require…

In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the…

In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…

In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion…

Construction on the measurement matrix $A$ is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

A random construction of bipolar sensing matrices based on binary linear codes is introduced and its RIP (Restricted Isometry Property) is analyzed based on an argument on the ensemble average of the weight distribution of binary linear…

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…

In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…

Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code $DG(m,r)$. This method of construction results in sensing matrices with low…

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…

Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a {\em separable} matrix. A…

Millimeter wave beam alignment (BA) is a challenging problem especially for large number of antennas. Compressed sensing (CS) tools have been exploited due to the sparse nature of such channels. This paper presents a novel deterministic CS…

It is well established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as…

In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathcal{H}^2$-matrices. We propose several new preconditioners…