Related papers: Low-Rank and Total Variation Regularization and It…

This paper studies the problem of aligning a set of face images of the same individual into a normalized image while removing the outliers like partial occlusion, extreme facial expression as well as significant illumination variation. Our…

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated…

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…

We present a low-rank transformation approach to compensate for face variations due to changes in visual domains, such as pose and illumination. The key idea is to learn discriminative linear transformations for face images using matrix…

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…

A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…

Rank-based Learning with deep neural network has been widely used for image cropping. However, the performance of ranking-based methods is often poor and this is mainly due to two reasons: 1) image cropping is a listwise ranking task rather…

Image restoration is the task of recovering a clean image from a degraded version. In most cases, the degradation is spatially varying, and it requires the restoration network to both localize and restore the affected regions. In this…

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…

Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…

In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…

Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…