Related papers: Bit Precision Analysis for Compressed Sensing
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.…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
This note studies the worst-case recovery error of low-rank and bisparse matrices as a function of the number of one-bit measurements used to acquire them. First, by way of the concept of consistency width, precise estimates are given on…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error…
One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
Consider the compressed sensing setup where the support $s^*$ of an $m$-sparse $d$-dimensional signal $x$ is to be recovered from $n$ linear measurements with a given algorithm. Suppose that the measurements are such that the algorithm does…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
Compressed Sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the…
The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Whereas classical compressed sensing algorithms do…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…