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In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Image denoising is a fundamental problem in image processing whose primary objective is to remove the noise while preserving the original image structure. In this work, we proposed a new architecture for image denoising. We have used…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…

The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function, and is the tighter approximation to matrix rank. However, most existing Schatten quasi-norm minimization (SQNM) algorithms, as well as for…

The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they…

Millimeter-wave radars are being increasingly integrated into commercial vehicles to support new advanced driver-assistance systems by enabling robust and high-performance object detection, localization, as well as recognition - a key…

This paper introduces a novel lightweight computational framework for enhancing images under low-light conditions, utilizing advanced machine learning and convolutional neural networks (CNNs). Traditional enhancement techniques often fail…

This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…

Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization…

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

The paper presents an image denoising scheme by combining a method that is based on directional quasi-analytic wavelet packets (qWPs) with the state-of-the-art Weighted Nuclear Norm Minimization (WNNM) denoising algorithm. The qWP-based…

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known…

Given an affine space of matrices $\mathcal{L}$ and a matrix $\Theta\in \mathcal{L}$, consider the problem of computing the closest rank deficient matrix to $\Theta$ on $\mathcal{L}$ with respect to the Frobenius norm. This is a nonconvex…

In this monograph, we review and develop variable projection Gauss-Newton, Levenberg-Marquardt and Newton methods for the Weighted Low-Rank Approximation (WLRA) problem, which has now an increasing number of applications in many scientific…

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the…

Large Language Models' (LLMs) weight matrices can often be expressed in low-rank form with potential to relax memory and compute resource requirements. Unlike prior efforts that focus on developing novel matrix decompositions, in this work…