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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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
39 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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29 views
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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1answer
29 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 \...
5
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0answers
155 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 ...
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0answers
21 views
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 ...
4
votes
1answer
93 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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vote
1answer
65 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 $y = h*x$. ...
0
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1answer
39 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 ...
2
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1answer
83 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?
2
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1answer
25 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 = \...
5
votes
1answer
139 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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0answers
15 views
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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0answers
18 views
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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64 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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57 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 ...
0
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1answer
86 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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24 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 ...
1
vote
1answer
44 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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0answers
30 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 ...
2
votes
1answer
52 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
139 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
79 views
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 ...
0
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1answer
47 views
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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40 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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44 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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0answers
78 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 CandĆØs, Terence Tao, Decoding by Linear ...
2
votes
1answer
131 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 ...
0
votes
1answer
48 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 ...
0
votes
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 ...
0
votes
1answer
81 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=Ī¦*x$ where $Ī¦$ is the sensing matrix.
I have used ...
3
votes
1answer
92 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$-...
2
votes
1answer
135 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 ...
4
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0answers
69 views
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 ...
2
votes
1answer
85 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 ...
2
votes
2answers
135 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 ...
1
vote
1answer
49 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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0answers
43 views
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 ...
0
votes
1answer
92 views
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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vote
2answers
347 views
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 ...
2
votes
2answers
146 views
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 ...
0
votes
2answers
88 views
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 ...
5
votes
1answer
233 views
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 ...
4
votes
2answers
509 views
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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vote
1answer
93 views
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 ...
9
votes
2answers
978 views
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 ...
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0answers
69 views
Sufficient conditions for exact signal recovery using OMP?
For a compressive sensing model :
$$y_{_{MXN}}=A_{_{MXN}}x_{_{NX1}}$$
where $x$ is $K$ sparse, what is the sufficient condition for Orthogonal matching Pursuit (OMP) to exactly recover the data for ...
3
votes
1answer
169 views
How to scale Phase Transition Diagram for Compressed Sensing?
I want to compute a Phase Transition Diagram as shown here ($A \in \mathbb{R}^{n \times N}$ and $k$ is the sparsity: $\vert \vert x \vert \vert_0 = k $ )
My question is: For $n=1$ I can only compute $...
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0answers
72 views
Iterative Hard Thresholding always thresholds same indices
I am confused by the fact that the thresholded indices in IHT do not change during the recovery. I used the code from this question and also added the condition that $$\vert \vert \Phi \vert \vert_2 &...
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vote
2answers
218 views
Why do we need deterministic measurement matrices in compressed sensing?
I recently introduced myself into the field of CS, but I do not understand why some people try to find deterministic measurement matrices?
If I am correct, gaussian random matrices are very powerful ...
