Signal Processing

Questions tagged [compressive-sensing]

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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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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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21 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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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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45 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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56 views

Sparsity Basis 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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39 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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49 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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61 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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78 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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95 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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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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70 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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86 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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36 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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40 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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41 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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159 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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104 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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79 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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174 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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358 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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68 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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684 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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63 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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145 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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63 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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163 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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62 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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302 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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56 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
278 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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238 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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1k 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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551 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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58 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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100 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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932 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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651 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
223 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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483 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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39 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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160 views

Real world application of signal sparsity?

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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383 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
130 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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263 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} $...
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202 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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877 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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107 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 ...
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239 views

Amplitude/phase recovery on noisy signal

I have a noisy signal that has an ac component of fixed frequency but variable amplitude and phase. I'd like to recover the ac component. The signal (blue trace) is mostly smooth, but has a few ...

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