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
If my measurement matrix have same number of row and column and the unkown vector is sparse can I still use Compressive Sensing to get better reconstruction with fewer measurement?
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1answer
22 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
115 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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12 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
15 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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0answers
50 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 ...
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1answer
73 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 ...
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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 ...
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1answer
45 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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106 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]
How would one implement the lock Orthogonal Matching Pursuit (BOMP) Algorithm?
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1answer
75 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 ...
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1answer
44 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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0answers
37 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
73 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
110 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
47 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 ...
0
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1answer
76 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
84 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
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1answer
124 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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0answers
67 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 ...
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1answer
81 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
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2answers
116 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
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1answer
42 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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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
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1answer
90 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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2answers
313 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 ...
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2answers
137 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 ...
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2answers
87 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
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1answer
213 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
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2answers
464 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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1answer
87 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 ...
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2answers
900 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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67 views
Sufficient conditions for exact signal recovery using OMP?
For a compressive sensing model :
$$y_{_{MXN}}=A_{_{MXN}}x_{_{NX1}}$$
where $x$ is $K$ sparse, what is the sufficient condition for Orthogonal matching Pursuit (OMP) to exactly recover the data for ...
3
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1answer
163 views
How to scale Phase Transition Diagram for Compressed Sensing?
I want to compute a Phase Transition Diagram as shown here ($A \in \mathbb{R}^{n \times N}$ and $k$ is the sparsity: $\vert \vert x \vert \vert_0 = k $ )
My question is: For $n=1$ I can only compute $...
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0answers
71 views
Iterative Hard Thresholding always thresholds same indices
I am confused by the fact that the thresholded indices in IHT do not change during the recovery. I used the code from this question and also added the condition that $$\vert \vert \Phi \vert \vert_2 &...
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2answers
210 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 ...
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0answers
63 views
Linear Systems, Sparse Solutions, and $4 \times 4$ Sudoku Algorithm [closed]
I am unable to understand the paper Linear Systems, Sparse Solutions, and Sudoku. I have to form a $4 \times 4$ Sudoku using the algorithm in this paper. Can somebody please provide me the algorithm ...
4
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1answer
478 views
Terminologies - sparse channel, sparse input, compressed sensing
The term sparse in general means that there are more elements that are zero valued or very close to zero in comparison to the number of non-zero. In speech deonvolution research papers, the channel ...
3
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1answer
65 views
Compression Sensing for Blind Source Separation
I am new to Signal Processing, and am interested in compression sensing for audio files. CS is based on the algorithm that, given some sampling of a signal $f$ in order to obtain a smaller (compressed)...
2
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1answer
325 views
Does the use of a sparse basis in Compressed Sensing imply the need to have access to all the information beforehand?
According to literature, the CS framework operates on the knowledge that most natural signals are sparse in some domain given by a sparsifying transform operation $\Phi$ (Fourier, Haar, WHT, etc.).
...
3
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2answers
327 views
Best Metric to Compare Sparsity of Vectors
I solved the Basis Pursuit Denoising Problem looking for a sparse solution (I am in compressive sensing):
$$ {x}^{\ast} = \arg \min_{x} \left\{ \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda ...
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1answer
2k views
How to implement compressed sensing reconstruction?
I am new to the field of Compressive Sensing. I'm trying to implement an example in this link. This example have described and implemented a sample tone reconstruction carefully, but unfortunately, ...
5
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1answer
644 views
Is the basis of the sparse signal assumed known in compressed sensing?
I'm new to compressed sensing, and am a little confused about the assumption of the basis matrix $\Psi$. Is $\Psi$ assumed known in compressed sensing?
Specifically, suppose that a signal $x$ is ...
1
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1answer
61 views
$l_2/l_2$ guarantee on sparse Fourier transform
I am starting my studies now on signal processing, and really didn't find nothing on "$l_2/l_2$ guarantee" of a certain function, in my case:
$$||\hat{x} - \hat{x}'||_2 \leq C\text{ min }_{\text{k-...
3
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1answer
103 views
Restriction of Fourier Transform
I am currently reading Candes et. al.'s 2006 paper[1] on recovery of sparse signals from incomplete frequency samples. I am having trouble figuring out what is the form of the Fourier transform ...
