Related papers: Reconstruction under outliers for Fourier-sparse f…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the…
This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…
Quantum computing promises exponential speedups for certain problems, yet fully universal quantum computers remain out of reach and near-term devices are inherently noisy. Motivated by this, we study noisy quantum algorithms and the…
We study reconstruction operators on a Hilbert space that are exact on a given reconstruction subspace. Among those the reconstruction operator obtained by the least squares fit has the smallest operator norm, and therefore is most stable…
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier…
It is well known that the class of rotation invariant algorithms are suboptimal even for learning sparse linear problems when the number of examples is below the "dimension" of the problem. This class includes any gradient descent trained…
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…
Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…
Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…
This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…
This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…
Functional near-infrared spectroscopy (fNIRS) is a non-invasive technique for monitoring brain activity. To better understand the brain, researchers often use deep learning to address the classification challenges of fNIRS data. Our study…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…
This paper considers the problem of recovering signals modeled by generative models from linear measurements contaminated with sparse outliers. We propose an outlier detection approach for reconstructing the ground-truth signals modeled by…
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…
In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to…