Related papers: The Noise-Sensitivity Phase Transition in Compress…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless…
We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Bounds on their performance, derived in the…
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…
We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
The problem of estimating an unknown phase $ \varphi $ using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. We introduce a simple model in which the phase-imprinting operation on…
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We consider the recovery of the signal $x_o \in \mathbb{R}^N$ from $n$…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
In this paper, we propose \textit{coded compressive sensing} that recovers an $n$-dimensional integer sparse signal vector from a noisy and quantized measurement vector whose dimension $m$ is far-fewer than $n$. The core idea of coded…