Related papers: Toeplitz Matrix Based Sparse Error Correction in S…
Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where…
In this article, we consider the problem of outlier-robust state estimation where the measurement noise can be correlated. Outliers in data arise due to many reasons like sensor malfunctioning, environmental behaviors, communication…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic…
Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has…
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a…
In this paper, we present an algorithm for effectively reconstructing an object from a set of its tomographic projections without any knowledge of the viewing directions or any prior structural information, in the presence of pathological…
We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…
The problems of uniform linear array (with uniform mutual coupling) calibration and Toeplitz covariance matrix estimation are re-examined for application in the receive arrays of modern High Frequency Over-the-Horizon Radars (HF OTHR).…
In this paper, we present an algorithm for effectively reconstructing an object from a set of its tomographic projections without any knowledge of the viewing directions or any prior structural information, in the presence of pathological…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…