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We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…

Numerical Analysis · Mathematics 2011-07-19 Massimo Fornasier , Holger Rauhut , Rachel Ward

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

Signal Processing · Electrical Eng. & Systems 2021-04-07 Cong Ma , Yuanxin Li , Yuejie Chi

We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…

Information Theory · Computer Science 2022-04-25 Sjoerd Dirksen , Johannes Maly , Holger Rauhut

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

We present a novel scheme allowing for 2D target localization using highly quantized 1-bit measurements from a Frequency Modulated Continuous Wave (FMCW) radar with two receiving antennas. Quantization of radar signals introduces…

Signal Processing · Electrical Eng. & Systems 2018-06-18 Thomas Feuillen , Chunlei Xu , Luc Vandendorpe , Laurent Jacques

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

Information Theory · Computer Science 2018-12-04 Yuanxin Li , Cong Ma , Yuxin Chen , Yuejie Chi

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…

Machine Learning · Computer Science 2023-10-18 Rajarshi Saha , Varun Srivastava , Mert Pilanci

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems,…

Numerical Analysis · Mathematics 2017-12-06 Yuling Jiao , Bangti Jin , Xiliang Lu

Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…

Optimization and Control · Mathematics 2024-04-23 Katherine Henneberger , Jing Qin

The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…

Numerical Analysis · Mathematics 2007-05-23 Thomas Strohmer , Roman Vershynin

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…

Numerical Analysis · Computer Science 2014-02-04 Hemant Kumar Aggarwal , Angshul Majumdar

There have been a number of studies on sparse signal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance.…

Information Theory · Computer Science 2013-05-21 Jun Fang , Yanning Shen , Hongbin Li

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Statistics Theory · Mathematics 2024-03-06 Xin Li , Dongya Wu

The design of sparse linear arrays has proven instrumental in the implementation of cost-effective and efficient automotive radar systems for high-resolution imaging. This paper investigates the impact of coarse quantization on measurements…

Signal Processing · Electrical Eng. & Systems 2024-03-07 Arian Eamaz , Farhang Yeganegi , Yunqiao Hu , Shunqiao Sun , Mojtaba Soltanalian

Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model.…

Information Theory · Computer Science 2019-02-13 Chunlei Xu , Laurent Jacques

The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we…

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…

Machine Learning · Statistics 2017-01-17 Xiao Zhang , Lingxiao Wang , Quanquan Gu

To conduct a more in-depth investigation of randomized solvers for solving linear systems, we adopt a unified randomized batch-sampling Kaczmarz framework with per-iteration costs as low as cyclic block methods, and develop a general…

Numerical Analysis · Mathematics 2026-04-21 Dong-Yue Xie , Xi Yang

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…

Optimization and Control · Mathematics 2013-04-26 B. Mishra , G. Meyer , R. Sepulchre

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…

Computer Vision and Pattern Recognition · Computer Science 2014-10-24 Xiaowei Zhou , Can Yang , Hongyu Zhao , Weichuan Yu