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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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help to troubleshoot an implementation of compressed sensing using L-BFGS and c++

i'm trying to reimplement the tutorial : http://www.pyrunner.com/weblog/2016/05/26/compressed-sensing-python/ i'm using the optimisation library from (https://ensmallen.org), to be more specific the ...
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1answer
37 views

Wireless body area networks with minimum energy consumption

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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50 views

Annihilating filter

For a signal $x_m$, consisting in a sequence of Diracs, this article proposes an annihilation filter $H(z)=\prod_{k=1}^{K}{(1-u_kz^{-1})}$ whose zeros are located in the exact location of the Diracs ...
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1answer
48 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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23 views

DCT based compressed sensing

** The formal definition of CS is y=Φx=ΦΨα where x is the input signals, Φ is the sensing matrix and y is the compressed vector. α is a sparse vector,and Ψ is a sparse basis. ** In case of DCT-...
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8 views

Two different definitions of coherence parameter

When we have the measurement basis $\varphi_{m \times n}$ and the sparse basis $\psi_{n \times n}$ the coherence parameter is defined as follows, $\mu_1(\varphi , \psi) = \sqrt{n}\max_{j,i}\frac{|\...
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1answer
64 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
50 views

Using the compressive 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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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
60 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
66 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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15 views

Square grids in single-pixel cameras

I have read a few research papers where the authors used Hadamard matrices as masks for image capture. In almost all of them the arrangement of the mask is square, e.g., some use a Hadamard $4096$ to ...
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1answer
32 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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29 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 ...
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1answer
30 views

Difference between Iteratively Reweighted Least Squares 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
52 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
86 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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19 views

Exact Sparse Reovery for a Special Measurement Matrix

I have a special case for Sparse Recovery. Here is the equation: [$B_2$$inv(B_1)$ I]x=y (1) Where $[B_1; B_2]s=z$, $B_1$ is square and full rank. $z$ is the observation vector. $y$ is the ...
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20 views

what is the difference between GOMP and BOMP?

Both group orthogonal matching pursuit (GOMP) and block orthogonal matching pursuit (BOMP) exploit the block sparsity to recover the signal. Is there any difference between these two algorithms?
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1answer
58 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 ...
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1answer
136 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 ...
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2answers
221 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
54 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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391 views

Sensing matrix in compressed sensing. Example in Python

So I'm following this example on how to compress a picture with compressed sensing. http://www.pyrunner.com/weblog/2016/05/26/compressed-sensing-python/ In the example, the picture is sparse in the ...
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2answers
409 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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60 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 ...
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1answer
119 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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47 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
108 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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58 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 ...
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1answer
103 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 ...
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44 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)...
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1answer
169 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.). ...
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2answers
190 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^* = \text{arg min}_x \left\{\frac{1}{2} \lVert Ax-y\rVert_2^2 + \lambda \lVert x\rVert_1\...
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1answer
771 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, ...
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1answer
374 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 ...
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1answer
50 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-...
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1answer
88 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 ...
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1answer
608 views

Sensing matrix for compressed sensing

What are the differences between random binary sensing matrix  and random Gaussian sensing matrix? What the advantages and disadvantages of each matrix? How can I choose the suitable matrix for a ...
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3answers
539 views

Difference between compressive sensing and DCT-based compression?

I am working on transmitting EEG signals over wireless body area network. I have applied two different compression techniques: DCT-based and compressive sensing (CS-based) approach. I noticed that the ...
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2answers
200 views

What are the practical constraints on designing Sensing matrix in compressed Sensing?

In a typical compressed sensing scenario, $y=Ax$, where $x$ is a sparse signal and $A$ is the sensing matrix. To reconstruct the sparse signal $x$ from $y$, $A$ should posses the Restricted Isometry ...
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2answers
416 views

Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

In the Compressed Sensing context, assume there is a signal $ x \in {\mathbb{R}}^{n} $ which is $ k $ sparse. Namely its Pseudo $ {\ell}_{0} $ Norm is $ {\left\| x \right\|}_{0} = k $ (The signal has ...
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38 views

Number of trials to judge performance of Compressive Sensing recovery algorithms

I'm trying to get a conclusive numerical value for Mean Squared Error (MSE) as the performance metric of a few CS sparse recovery algorithms. To do this, I vary the number of measurements ($M$) taken ...
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2answers
108 views

Real world application of signal sparsity other than Cognitive Radio?

There are theories based on signal sparsity in frequency domain like Compressive Sensing, Sparse FFT, etc. Throughout searching and studying papers I found out Cognitive Radio is a good example of ...
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1answer
274 views

Signal sparsity: with noise or without noise?

In compressive-sensing, signal should be sparse. Is this with or without noise? When I differentiate signal, it is supposed to be sparse. But when I add noise on it, it isn't sparse anymore. Should ...
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1answer
118 views

Estimation of occupied frequency bins (location of non-zero fourier coefficients)

I'm working in circuits fields and I am not very familiar with spectrum sensing techniques. Is there a method to identify location of non-zero Fourier coefficients of a signal (just locations, not ...
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1answer
228 views

Approximating $ {L}_{0} $ Norm Minimization with Non Linear Convex Inequality Constraints using Reweighted $ {L}_{1} $ Minimization

I have an optimization problem consisting of the $ {\ell}_{0} $ norm as the objective and a nonlinear (convex) constraint as well as a linear constraint. I am wondering if the reweighted $ {\ell}_{1} $...
4
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1answer
172 views

Relationship between information retrieval and source separation in signal processing

In machine learning, for the task of classifying input data (called an example) which are in binary representation, $\mathbf{x}\in \mathbb{R}^D$, $\mathbf{x} \in \{0,1\}^D$ into its multiple class ...
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2answers
633 views

Seeking compressive sensing imaging demo in MATLAB

I am looking to experiment in MATLAB with image restoration/reconstruction using compressed sensing. I am relatively new to compressive sensing, and was inspired by the following Wired article to ...
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1answer
88 views

How we can encode/decode sparse signals?

I have question and looking for help. Suppose we have a vector of real values (lat's say 64 length resulting from factorization 8*8 block image). We got a sparse representation of that vector (let's ...