Related papers: The Quasi-probability Method and Applications for …
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Accurate determination of particle track reconstruction parameters will be a major challenge for the High Luminosity Large Hadron Collider (HL-LHC) experiments. The expected increase in the number of simultaneous collisions at the HL-LHC…
Recent advances in segmented solid-state detector arrays for rare-event searches have allowed the technology to approach the ton-scale in detector mass and the scale of meters in size. Often focused around searches for neutrinoless…
We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction, but also a covariance matrix…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…
The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it…
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has…
An approximate sparse recovery system in $\ell_1$ norm consists of parameters $k$, $\epsilon$, $N$, an $m$-by-$N$ measurement $\Phi$, and a recovery algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates $x$ by…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…
In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…
We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix. It is known that the cost of l1-norm minimization using a…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb…