Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [compressive-sensing]

the field of study that aims to solve an underdetermined linear system of equations by exploiting the structure of the unknown data

142 questions
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Is there any alternative characterization of sparsity of a signal in compressed sensing

The starting assumption for compressed sensing (CS) is that the underlying signal is sparse in some basis, e.g., there are a maximum of non-zero Fourier-coefficients for an $s$-sparse signal. And real life experiences do show that the signals…
Arnab
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Does an asymmetric Bernoulli matrix satisfy the RIP?

Define an $n\times N$ sensing matrix $A$ by $A_{ij} = 0$ with probability $p$, and $A_{ij} = 1/\sqrt{n}$ with probability $1-p$. Does $A$ satisfy the restricted isometry property? For reference, the symmetric case is answered in the following…
olivia
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Restricted Isometry Property (RIP) in Compressive Sensing

What is the meaning of Restricted Isometry Property (RIP) condition in Compressive Sensing for Sparse Signal Analysis? How can we define Restricted Isometry Constant (RIC) for the RIP condition? Thanks in Advance!
tuner
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Conditions for unique (not exact) recovery from noisy compressed measurements

I am looking for theory on whether compressed sensing reconstruction via ℓ1-minimization is unique and under which conditions. I have looked through: Tropp, J. A., "Just relax: convex programming methods for identifying sparse signals in noise,"…
Thomas Arildsen
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What is the tightest known bound on the reconstruction error in compressed sensing?

I am specifically thinking about the reconstruction error of L1-minimization from compressed measurements with noise. I know a bound from (8) in The restricted isometry property and its implications for compressed sensing, but I was wondering if…
Thomas Arildsen
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Why doesn't compressive sensing work for any signal?

My (probably naive) understanding of compressive sensing is that it is a technique that allows to efficiently reconstruct an $N$-dimensional signal $\boldsymbol x$, provided that it is sparse in some basis (without the need to know the sparsity…
glS
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Signal Acquisition in Compressed Sensing

I'm trying to wrap my head around compressed sensing, so I've been reading this intro to the topic. I'm completely keeping up when they discuss exploiting the sparsity of a signal in some domain to compress it. I also think I get why you'd want to…
John Vinyard
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Smart way to sample in "time domain" for a known "frequeny domain"

I have an experiment in which every point in the "time domain" is very expensive to take. Good news is I know the center frequency and the bandwidth of the signal. How can I sample (which times should I probe) in the time domain to get the most…
Gyromagnetic
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Compressive sensing: numerical generation of RIP matrices

The restricted isometry property (RIP) states that: \begin{equation} (1-\delta_K)||x||_2^2 \le ||A x||_2^2 \le (1+\delta_K)||x||_2^2 \end{equation} for any $K$-sparse vector $x$ of length $N$. The corresponding restricted isometry constant is…
gbarr
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Compressed Sensing and Sparsity

Ok for first information I would like to let you know that I originally do not have any formal exposure in signal processing so I would appreciate if you consider me as a beginner. In particular in this project I have to deal with the method of…
Tommy 77
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Combining compressed measurements from the same source

Suppose I want to measure a signal $x \in \mathbb{R}^n$ subject to i.i.d. noise $\epsilon$. In traditional Nyquist Sampling, I can increase my signal-to-noise ratio by measuring $x + \epsilon$ for $k$ times and averaging over the measurements.…
Mr Vinagi
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How to scale Phase Transition Diagram for Compressed Sensing?

I want to compute a Phase Transition Diagram as shown here ($A \in \mathbb{R}^{n \times N}$ and $k$ is the sparsity: $\vert \vert x \vert \vert_0 = k $ ) My question is: For $n=1$ I can only compute $k=1$, for $n=2$ I can only compute $k=1,2$ and so…
N8_Coder
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Compressive Sensing - Location of Non Zero Elements

I am new in compressive sensing and I would like to know if there already exists a deterministic or probabilistic approach to estimate the locations of the $k$ non-zero entries in the $k$-sparse vectore $x$.
user2987
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Restricted Isometry (non-sparse)

Let $x$ be a $N \times 1$ vector in $\mathbb{R}^{N}$ where $M$ components are zero and the remaining $N-M$ components are standard normal random variables. $x$ may not be sparse e.g. $M$ may be small. I am interested in bounding $||Ax||_{l_{2}}$…
Mykie
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update the image plane distance in Fresnel transform

I have performed reconstruction of images in Fresnel transform using a desired algorithm. Now the aim is to find an optimal value of image plane distance at which the reconstruction is accurate. I have formulated the problem as below: ||X_recon -…
budding_scholar
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