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

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Compressive sensing based sparse vector estimation

I am newbie in compressive sensing (CS), I read about compressive sensing and its use for sparse vector estimation. As I understood CS can be used either in time or frequency domain. For me, The part ...
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Compressing sparse vectors based on compressive sensing

I have a sparse vector $x$ of size $N$x$1$ which is sparse with number of non-zeros values are $m$, it means $m$ out of $N$ values are non-zeros, the non-zeros locations are distributed randomly. ...
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Single Pixel Camera - Compressive Sensing

I work with a setup that measures high frequency fluctuations in light using a photodiode. We steer the light over a sample as we measure these fluctuations. I am familiar with compressive sensing ...
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Advantages and disadvantages of multiplying sparse vector with sparse matrix

Assume I have a sparse vector $x$ whose few values are non-zeros, that vector is multiplied with sparse unitary matrix $Y$ giving $z = Yx$. Are there any advantages of detecting the sparse vector $x$ ...
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Estimating Convolution Input Under the Assumption of Sparsity and Constant Non Zero Values Using Compressive Sensing Approach

I was wondering about if there is compressive sensing algorithm to estimate the sparse vector where the number of non-zeros values and amplitude of every non-zeros value are known. For example, assume ...
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Sparse recovery, Restricted Isometry Property for ILL-POSED problems

if $\mathbf x$ is $N\times 1$ sparse vector, and $\mathbf A$ is an $M\times N$ matrix with $M<<N$, and we measure $\mathbf y=\mathbf{Ax}$, then compressed sensing theory tells us that we can ...
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How to Generate Sensing Matrix with Variable Probabilities on Fourier Domain?

Recently, I found a good resource of Compressed Sensing applying on MRI, Michael (Miki) Lustig - Compressed Sensing MRI Resources. The variables "pdf_unif" and "pdf_vardens" store the probabilities of ...
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Solving LASSO (Basis Pursuit Denoising Form) with LARS

I'm now working on using LARS (Least Angle Regression) algorithm to solve a LASSO problem in Basis Pursuit Denoising form like: \begin{align*} \quad && \arg \min_{\beta}{\left\| y - X\beta \...
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Residual error when setting measurement matrix in compresssive sensing

I have an issue when implementing compressive sensing to recover sparse vector. Assume I have sparse vector $x$ of length, for example, $(256,1)$. $x = [x_1,x_2,.....x_{256}]$. This vector is ...
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The reconstruction of probabilistically sparse signals

Consider we have a vector $\boldsymbol{x}_1^n$ which has a sparse structure in the sense that \begin{equation} \mathbb{P}(x_i=0)=\alpha>0. \end{equation} Further, assume that we have a sampled ...
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On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
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Projecting a vector to another to detect the sparse values of such vector

Assuming we have sparse vector of length $N$ such as $X = [0,1,0,-1,0,1,1,0]$ which has some non-zeros values. The vector $x = iFFT(X)$ is convoluted with another vector $h$ resluting $y = h*x$. ...
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On the Use of OMP Algorithm to Estimate Sparse Vector

As known, Orthogonal Matching Pursuit (OMP) Algorithm is to recover the sparse channel after convolution with another vector. But when I implement that in MATLAB, I don't get the sparse vector ...
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Compressive Sensing with Square Measurement Matrix

If my measurement matrix have same number of row and column and the unknown vector is sparse can I still use Compressive Sensing to get better reconstruction with fewer measurement?
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applicability of dictionary learning in compressed sensing problem

Compressed Sensing Problem: $Y = MX$, $M$ = measurement matrix (known), $X$ = full signal (unknown), $Y$ = sampled points (known). Objective is to obtain $X$ using the concept of sparsity i.e. $X = \...
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Can compressed sensing be used instead of intepolation for missing values?

Consider a signal that is sparse in frequency, but it measured in the time domain, for example (in matlab): ...
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Compressed Channel Sensing

I am going through the fundamentals and the state-of-the-art mmwave protocols and research. I came across Compressed Channel Sensing. For sparse multipath structured channel compresssed sensing is ...
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Can the mutual coherence of a matrix be used to determine the number of measurements required in compressive sensing

We know that in compressive sensing, the RIP property is very difficult to determine in practice, so instead we rely on the weaker property of the mutual coherence of the sensing matrix. Let's say I ...
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Analog-to-Information Converters?

In Analog-to-Digital Converters(ADC), the signal is first sampled at a rate higher than or equal to the Nyquist, then quantized and encoded. In Analog-to-Informations (AIC), the sampling and ...
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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 ...
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Orthogonal Basis for a 2D Signals (Compressive Sensing)

I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2). I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
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Rakeness Optimization problem

Rakeness optimization problem demonstrate that increases the rakeness between a , b while leaving b random enough. where e is the energy of the projection waveforms and r is a randomness-enforcing ...
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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 $k$ ...
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What is the best way to separate data using compressive sensing?

In the book Compressed Sensing by Kutyniok et al, the author talks about data separation using sparse representation. In summary, if we have a signal vector $x = x_1 + x_2$ Then, it would be ...
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Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
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Why Does FISTA Algorithm Not Work for Signed Signals?

Using the FISTA Algorithm for compressive sensing from https://github.com/tiepvupsu/FISTA, I created the matlab example below. I created 2 sparse signals x_signed and x_pos, where the latter only ...
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Resources on Solving Convex Optimization Problems in the Compress Sensing Field

When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge ...
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why restricted isometry property constant $\delta_{2k}<\sqrt{2}-1$?

It's said that $\delta_{2k} < \sqrt{2} -1$ , the solution of the $l_{1}$ problem is that of $l_{0}$ problem. I checked the proof of $||x^{*}-x||_{l_{2}}\leq C_{0}s^{-1/2}||x-x_{s}||_{l_{1}}+C_{1}\...
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What is the error rate in compressed sensing?

Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by $$y=Ax$$ Let $\hat{x}$ be defined as follows $$\hat{x}:=\arg\min_{z\...
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The origin of the restricted isometry property (RIP)

I have been looking for the origin of the restricted isometry property (RIP). Many papers cite the origin of the RIP in the following paper Emmanuel Candès, Terence Tao, Decoding by Linear ...
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Sparsity Representation of a Signal Using the DCT Matrix

I have a signal $\mathbf x$, and I need to know how to obtain the matrix which is the corresponding sparsity basis $\mathbf\Psi$ such that $\mathbf x = \mathbf{\Psi\theta}$, where $\mathbf\theta$ is ...
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Coherence Calculation in Sparse Sensing

i have an image I of size 32*32. I perform the DCT of this image using the matlab function DCT2(I). I get a sparse representation of my image which is again a 32*32 image. I construct a circulant ...
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Wireless Body Area Networks with Minimum Energy Consumption [closed]

For adaptive compressive sensing(cs),the sensing matrix is related to the input signal. For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ...
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Energy of compressed signals

I have tried a code to compress a signal using Compressed Sensing(CS). The input signal is $x$ and the compressed signal $y$ is given by : $y=Φ*x$ where $Φ$ is the sensing matrix. I have used ...
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How Is Mixed Norm ($ {L}_{1, 2 }$) Better than $ {L}_{1} $ Norm for Sparse Representation?

Using $ {l}_{1} $-norm regularization for the purpose of achieving sparsity of the solution has been successfully applied a lot. But many times, I found the paper using mixed-norm instead of $l_1$-...
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Compressed Sensing Mathematical Concept in Signal Processing

I am new in the field of compressive sensing, I've read many papers explaining that compressive sensing is used widely in sparse signal reconstruction. I've tried to understand how compressive sensing ...
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Designing a fast linear operator with $\pm 1$ entries with low condition number and low Hamming distance between consecutive rows

I need to design a matrix for compressive imaging where each row represents an $N$-pixel filter in a focal plane through which light is masked, summed, and measured (think of Rice's single-pixel ...
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Sparse Recovery Best Algorithms

In the big data era, in order to control the cost, complexity, and bandwidth of collecting and processing high-dimensional data systems, it is critical to exploit models that ...
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Compressive Sensing and Sparsity

We apply compressive sensing to reconstruct a signal if it is sparse in the original domain or has a sparse represetation in some basis. How we may know a if a signal is sparse or has a sparse ...
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What Is Adaptive Compressive Sampling?

I have just started my work in compressive sensing. the measurement vectors are obtain by multiplying the sensing matrix with input signal. the thing i cant figure out adaptive compressive sampling. ...
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Required number of measrments for signal recovery in a compressed sensing MMV problem?

For multiple measurement vector (MMV) problem $Y=AX$ where $A$ is $m \times n$ sensing matrix and $X$ is $n \times L$ matrix haveing K non zero rows. What are the necessary conditions on the ...
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Difference Between Iteratively Reweighted Least Squares (IRLS) and Sequential Quadratic Programming?

Part of my work is concerned with applications in Sparse Bayesian Learning and therefore I occasionally stumble over interesting papers in the field of compressed sensing. I recently read ...
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Compressive Sensing - Sparse in frequency example

I am learning about compressed sensing. I have a question regarding a common MATLAB "sparse in frequency" example that can be find online, for example here and here. What confuses me in these ...
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Higher-order Kronecker product

I am trying to generate a 2D DFT matrix in matlab, which I need for 2D compressed sensing (CS) problems. Lets say $N_1=8$, $N_2=16$, then according to the requirement of CS, to generate a 2D DFT ...
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Compressive Sensing: Reconstruct Gap in Antenna Array

I have an antenna array with $N$ elements spaced half a wavelength apart. I have a second, identical antenna array that is the distance $D$ apart from the first one. Could I use compressive sensing ...
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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 ...
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Reference Code for Positive Basis Pursuit Denoising

I am trying to reconstruct a positive sparse signal using compressed sensing (friedlanders code), I cannot find a way to impose the positivity constraint for this implementation. I have seen some ...
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Sub nyquist sampling, required number of samples for time sparse grouped signals

Question: Does it make sense to perform compressed sampling if the non zero samples are grouped in time? If so, what is the minimal length of the vector x that should be acquired to allow full signal ...
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Compressive Sensing vs. Sparse Coding

There apparently are different terminologies used to refer to the same field called "compressive sensing" such as (see this wiki page): compressed sensing, compressive sampling, or sparse sampling. I ...