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Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
Transformer architectures show spectacular performance on NLP tasks and have recently also been used for tasks such as image completion or image classification. Here we propose to use a sequential image representation, where each prefix of…
It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…
We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and…
In this paper, we investigate the problem of recovering the frequency components of a mixture of $K$ complex sinusoids from a random subset of $N$ equally-spaced time-domain samples. Because of the random subset, the samples are effectively…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
The low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This…
We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target…
We propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality.…
Can one recover a matrix efficiently from only matrix-vector products? If so, how many are needed? This paper describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz-like, and hierarchical…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…
This paper investigates how to recover parameters of a linear time invariant system from values and derivatives of its transfer function matrix, along several particular directions at a prescribed set of points in the complex plane, in…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…
The combination of the sparse sampling and the low-rank structured matrix reconstruction has shown promising performance, enabling a significant reduction of the magnetic resonance imaging data acquisition time. However, the low-rank…
This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the…