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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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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40 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
48 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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1answer
37 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
46 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
59 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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1answer
74 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
79 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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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
68 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
82 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
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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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
40 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
139 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
102 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
73 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
166 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
316 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
64 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
622 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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62 views
Sufficient conditions for exact signal recovery using OMP?
For a compressive sensing model :
$$y_{_{MXN}}=A_{_{MXN}}x_{_{NX1}}$$
where $x$ is $K$ sparse, what is the sufficient condition for Orthogonal matching Pursuit (OMP) to exactly recover the data for ...
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1answer
140 views
How to scale Phase Transition Diagram for Compressed Sensing?
I want to compute a Phase Transition Diagram as shown here ($A \in \mathbb{R}^{n \times N}$ and $k$ is the sparsity: $\vert \vert x \vert \vert_0 = k $ )
My question is: For $n=1$ I can only compute $...
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0answers
60 views
Iterative Hard Thresholding always thresholds same indices
I am confused by the fact that the thresholded indices in IHT do not change during the recovery. I used the code from this question and also added the condition that $$\vert \vert \Phi \vert \vert_2 &...
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2answers
143 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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61 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
253 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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0answers
50 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
262 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
228 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):
$$ x^* = \text{arg min}_x \left\{\frac{1}{2} \lVert Ax-y\rVert_2^2 + \lambda \lVert x\rVert_1\...
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1answer
1k views
How to implement compressed sensing reconstruction?
I am new to the field of Compressive Sensing. I'm trying to implement an example in this link. This example have described and implemented a sample tone reconstruction carefully, but unfortunately, ...
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1answer
521 views
Is the basis of the sparse signal assumed known in compressed sensing?
I'm new to compressed sensing, and am a little confused about the assumption of the basis matrix $\Psi$. Is $\Psi$ assumed known in compressed sensing?
Specifically, suppose that a signal $x$ is ...
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1answer
56 views
$l_2/l_2$ guarantee on sparse Fourier transform
I am starting my studies now on signal processing, and really didn't find nothing on "$l_2/l_2$ guarantee" of a certain function, in my case:
$$||\hat{x} - \hat{x}'||_2 \leq C\text{ min }_{\text{k-...
4
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1answer
98 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
853 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
635 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
220 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
463 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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0answers
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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3answers
154 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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1answer
370 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 ...
3
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1answer
125 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
251 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
197 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
838 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
102 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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226 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 ...
2
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1answer
102 views
Compressive Sensing: location of non-zero elements
I am new in compressive sensing and I would like to know if there already exists a deterministic or probabilistic approach to estimate the locations of the $k$ non-zero entries in the $k$-sparse ...
3
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2answers
757 views
Compressive sensing: numerical generation of RIP matrices
The restricted isometry property (RIP) states that:
\begin{equation}
(1-\delta_K)||x||_2^2 \le ||A x||_2^2 \le (1+\delta_K)||x||_2^2
\end{equation}
for any $K$-sparse vector $x$ of length $N$. The ...
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2answers
136 views
Transform matrix creation in compressed sensing
In Compressed sensing ECG reconstruction I would like to use biorthogonal wavelet basis as transform/sparsifying domain. I found out that wfilters command in MATLAB ...
