Related papers: Square Root Principal Component Pursuit: Tuning-Fr…
We consider a high dimensional linear regression problem where the goal is to efficiently recover an unknown vector $\beta^*$ from $n$ noisy linear observations $Y=X\beta^*+W \in \mathbb{R}^n$, for known $X \in \mathbb{R}^{n \times p}$ and…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
In this paper, we put forth a new joint sparse recovery algorithm called signal space matching pursuit (SSMP). The key idea of the proposed SSMP algorithm is to sequentially investigate the support of jointly sparse vectors to minimize the…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measurements. Our results are applicable for symmetric rank-one…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…
Crucial information barely visible to the human eye is often embedded in a series of low-resolution images taken of the same scene. Super-resolution enables the extraction of this information by reconstructing a single image, at a high…
We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…
This work studies the recursive robust principal components' analysis (PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this…
Lasso is a seminal contribution to high-dimensional statistics, but it hinges on a tuning parameter that is difficult to calibrate in practice. A partial remedy for this problem is Square-Root Lasso, because it inherently calibrates to the…
In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two…