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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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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38 views
How do I find the Inverse Fourier matrix?
Suppose that y = φx where y's length is K x 1, φ's length is K x N and φ's length is N x 1.
The above can be expressed as a sparse vectors in the Fourier domain, x = Ψs.
y = φΨs where Ψ's length is N ...
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1answer
51 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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1answer
46 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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31 views
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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25 views
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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1answer
37 views
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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1answer
183 views
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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57 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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2answers
44 views
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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1answer
34 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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57 views
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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77 views
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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28 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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1answer
150 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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1answer
122 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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2answers
139 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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1answer
85 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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1answer
87 views
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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171 views
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 ...
5
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1answer
123 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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1answer
76 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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1answer
59 views
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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1answer
104 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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1answer
26 views
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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1answer
235 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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98 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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59 views
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 ...
3
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1answer
189 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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27 views
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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1answer
49 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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31 views
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 ...
3
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1answer
69 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]
This is my implementation which doesn't work:
...
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2answers
234 views
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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1answer
111 views
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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1answer
86 views
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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56 views
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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47 views
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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119 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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1answer
214 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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1answer
59 views
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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1answer
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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1answer
96 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 ...
3
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1answer
205 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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1answer
166 views
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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1answer
101 views
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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2answers
144 views
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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1answer
55 views
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 ...
