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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Compressed Sensing -- reproducing simple 1-D example [python]

Context Attempting to reproduce an illustrative example of compressive sampling from Candes-Wakin 2008. Specifically, the L1 recovery of a sparse signal shown on pg 5 in Fig. 2. Using my code (below), ...
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Can we use AutoEncoder for Sparse Sensing?

Is there a way to introduce sparsity constraint on an autoencoder to achieve compressions in the Cosine/Fourier domain? I want to use the encoder part of the Auto encoder as the feature extractor from ...
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K-SVD Implementation Based on Measurements of signal

How can the K-SVD algorithm be implemented by using measurements y of signal vector x? The goal is to minimize $$ \|y-\phi BZs\|, $$ with $Y$ the measurements of signal matrix X, $\phi$ the ...
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compressed sensing versus Lomb-Scargle

Say I have a signal that's the sum of only a few sine/cosine waves, and some noise, which has been measured at random times. I would like to find the frequencies of the waves. With this goal in-mind, ...
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How to find the number of vectors to sample in Compressed Sensing?

When comparing my MATLAB code to a previously written one, I come across the following formula for the number of vectors to sample: ...
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How can we interpret Spatial Cross Correlation between two images in case of compressed sensing based reconstruction of images?

I am reconstructing images using compressed sensing. The images are used from sipi database. One particular image, named Female Bell Lab, which is giving better result with high PSNR around 42 dB and ...
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How to find the Wavelet measurement matrix in compressed sensing?

Assume that an image vector x = Ψs. s is a sparse vector in which the image vector x of length N x 1 is sparse in the wavelet Ψ basis. I have issue in finding the measurement matrix A= φ Ψ where φ is ...
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56 views

Can a linear reconstruction in compressive sensing perform well?

I am trying to implement compressive sensing for grayscale 2D images, then reconstructing them using a multi-layer perceptron(MLP). It seems to perform well no matter how many layers I add or remove, ...
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53 views

Why is incoherence important for compressive sensing?

The literature on compressive sensing (CS) frequently notes that CS relies on two principles: sparsity and incoherence. While I understand why the signal of interest should be sparse in some domain ...
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What is an analysis dictionary or operator in compressive sensing?

I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries. Here are some papers that I have read so far: https://www.hindawi.com/...
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RIPless Compressive Sensing - Proof of Incoherence Sampling Theorem

It is the first time I'm facing this topic. In particular, I'm studying the RIPless framework of compressive sensing presented by Emmanuel J. Candès and Yaniv Plan in the article https://arxiv.org/...
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Is it common to impose the sparsity on the Fourier coefficient itself?

In compressive sensing, I see many works to impose the sparsity on the wavelet coefficients (e.g., by minimizing the L1 norm of such coefficients.) Another example in MRI is to impose sparsity on the ...
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Super Resolution in Frequency Domain Using Compressed Sensing

To be noted that I'm very new to this topic, I would like to understand the fundamentals of how to get Super Resolution in Frequency Domain estimation using the Compressed Sensing Model. I am also ...
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60 views

Compressed Sensing in DOA processing

I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing I use a first FFT to solve the range ...
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What do you call the random Gaussian vectors in compressed sensing?

Let $(e_i)_{1\leq i\leq M}$ be vectors with zero-mean i.i.d. entries from a Gaussian distribution. In a compressed-sensing setup, I have observed the collection of scalar products $(\langle x\, |\, ...
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35 views

Preserve specific information in compressed sensing

I have a signal that isn't perfectly sparse and I would like to apply compressed sensing on it for lossy compression. However I would like to preserve specific section of the signal so that this "...
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Coefficient in Sparse Signal Recovery

To understand the idea of sparse signal recovery described in Sparsity and Incoherence in Compressive Sampling, I decided to build a toy problem. Suppose the sparse signal that we want to reconstruct $...
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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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33 views

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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196 views

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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128 views

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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141 views

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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94 views

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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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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1answer
128 views

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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78 views

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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105 views

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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249 views

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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112 views

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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195 views

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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50 views

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 Tiep H. Vu - FISTA, I created the matlab example below. I created 2 sparse signals x_signed and x_pos, where the latter only contains positive ...
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Resources on Solving Convex Optimization Problems in the Compressed 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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129 views

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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231 views

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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52 views

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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98 views

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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254 views

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 ...