Related papers: Joint Reconstruction and Low-Rank Decomposition fo…
This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited…
Objective: Interventional MRI (i-MRI) is crucial for MR image-guided therapy. Current image reconstruction methods for dynamic MR imaging are mostly retrospective that may not be suitable for i-MRI in real-time. Therefore, an algorithm to…
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…
Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
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,…
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to…
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…
Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…
The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent…
Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, Non-negative Implicit Neural…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with 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…