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We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an…
Given full or partial information about a collection of points that lie close to a union of several subspaces, subspace clustering refers to the process of clustering the points according to their subspace and identifying the subspaces. One…
While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously…
During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and…
This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
We present a smooth probabilistic reformulation of $\ell_0$ regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, facilitating rapid convergence to local optima of the best…
Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…
To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing based wireless sensor networks. In the proposed approach,…
The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, "structure" is represented by sparsity in some known basis. Inspired by…
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…
The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…
We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…
We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. Our approach is based on applying an optimal "denoiser"…
Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper…