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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Discussion "Recovering Low-Rank Matrices From Few Coefficients In Any Basis"

Existing work concentrated mostly on the problem of “matrix completion” where one aims to recover a low-rank matrix from randomly selected matrix elements. Their result covers this situation as a ...
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6 votes
3 answers
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What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The Fourier basis is a common choice for transformations, but a lot of times, it's not the best for a specific application. For instance, wavelet bases give us better spatial / temporal locality than ...
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update the image plane distance in Fresnel transform

I have performed reconstruction of images in Fresnel transform using a desired algorithm. Now the aim is to find an optimal value of image plane distance at which the reconstruction is accurate. I ...
2 votes
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How to build the measurement matrix used for compressive sensing

I have a sparse vector $x \in \mathbb{R}^{N \times 1}$, it's real and positive, the non-zeros values are maximum $N/2$ values. It means, I have at least $N/2$ zeros values in $x$. My question, is it ...
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Universal bases (dictionary) for image compression

I am a physics graduate student working on a data compression problem. I have been reading Prof. Steven L. Brunton's book on data driven science and engineering. I am fascinated to the concept of ...
8 votes
1 answer
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Clear understanding of compressed sensing

I am trying to get a clear understanding of how compressed sensing works. A continuous signal $x(t)$ is under-sampled (less samples are collected than the numbers required by the Nyquist theorem). The ...
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Coherence in compresive sensing

I am starting to write my master thesis, and it's in field of compressive sensing. I have some problems with math behind it. I don't understand the concept of matrix coherence. I know how it is ...
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Does good reconstruction of CS promise smaller isometry constant?

I'm a newbie to compressed sensing, here is my question. If measurement matrix $A$ satisfies RIP with a minor $\delta_{2k}$, which should be < 1, then there is a unique $k$-sparse solution. But if $...
3 votes
1 answer
55 views

Is it possible to detect the sparse vector based on a non-invertible matrix

Given a non-invertible matrix $X \in \mathbb{R}$, let's say that matrix is, e.g. : $X = \begin{bmatrix} 0.7500& -0.2500 &-0.2500 & -0.2500 \\ -0.2500& 0.7500& -0.2500 & -0....
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How to remove noise from the signal? [closed]

I'm new to DSP and currently working on time-series data. The mentioned time series (of Toe) is extracted from a video tracking various body parts of an athlete. Ideally, there shouldn't be any ...
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Random projection with compressive sensing and hashing algorithms

I read that Random Projection matrices can be used in both Compressive Sensing and Locality Sensitive Hashing. I need simple explanation for the difference between applying Random Projection in both ...
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Reconstruction of a Signal from Sub Sampled Spectrum by Compressed Sensing

Context Attempting to reproduce an illustrative example of compressive sampling from Candes-Wakin 2008. Specifically, the L1 recovery of a sparse signal shown on pg 5 in Fig. 2. Using my code (below), ...
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Can we use AutoEncoder for Sparse Sensing?

Is there a way to introduce sparsity constraint on an autoencoder to achieve compressions in the Cosine/Fourier domain? I want to use the encoder part of the Auto encoder as the feature extractor from ...
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compressed sensing versus Lomb-Scargle

Say I have a signal that's the sum of only a few sine/cosine waves, and some noise, which has been measured at random times. I would like to find the frequencies of the waves. With this goal in-mind, ...
1 vote
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How to find the Wavelet measurement matrix in compressed sensing?

Assume that an image vector x = Ψs. s is a sparse vector in which the image vector x of length N x 1 is sparse in the wavelet Ψ basis. I have issue in finding the measurement matrix A= φ Ψ where φ is ...
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Can a linear reconstruction in compressive sensing perform well?

I am trying to implement compressive sensing for grayscale 2D images, then reconstructing them using a multi-layer perceptron(MLP). It seems to perform well no matter how many layers I add or remove, ...
3 votes
1 answer
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Why is incoherence important for compressive sensing?

The literature on compressive sensing (CS) frequently notes that CS relies on two principles: sparsity and incoherence. While I understand why the signal of interest should be sparse in some domain ...
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What is an analysis dictionary or operator in compressive sensing?

I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries. Here are some papers that I have read so far: https://www.hindawi.com/...
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Is it common to impose the sparsity on the Fourier coefficient itself?

In compressive sensing, I see many works to impose the sparsity on the wavelet coefficients (e.g., by minimizing the L1 norm of such coefficients.) Another example in MRI is to impose sparsity on the ...
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Super Resolution in Frequency Domain Using Compressed Sensing

To be noted that I'm very new to this topic, I would like to understand the fundamentals of how to get Super Resolution in Frequency Domain estimation using the Compressed Sensing Model. I am also ...
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Compressed Sensing in DOA processing

I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing I use a first FFT to solve the range ...
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What do you call the random Gaussian vectors in compressed sensing?

Let $(e_i)_{1\leq i\leq M}$ be vectors with zero-mean i.i.d. entries from a Gaussian distribution. In a compressed-sensing setup, I have observed the collection of scalar products $(\langle x\, |\, ...
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Preserve specific information in compressed sensing

I have a signal that isn't perfectly sparse and I would like to apply compressed sensing on it for lossy compression. However I would like to preserve specific section of the signal so that this "...
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Coefficient in Sparse Signal Recovery

To understand the idea of sparse signal recovery described in Sparsity and Incoherence in Compressive Sampling, I decided to build a toy problem. Suppose the sparse signal that we want to reconstruct $...
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Compressive sensing based sparse vector estimation

I am newbie in compressive sensing (CS), I read about compressive sensing and its use for sparse vector estimation. As I understood CS can be used either in time or frequency domain. For me, The part ...
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Compressing sparse vectors based on compressive sensing

I have a sparse vector $x$ of size $N$x$1$ which is sparse with number of non-zeros values are $m$, it means $m$ out of $N$ values are non-zeros, the non-zeros locations are distributed randomly. ...
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Single Pixel Camera - Compressive Sensing

I work with a setup that measures high frequency fluctuations in light using a photodiode. We steer the light over a sample as we measure these fluctuations. I am familiar with compressive sensing ...
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Advantages and disadvantages of multiplying sparse vector with sparse matrix

Assume I have a sparse vector $x$ whose few values are non-zeros, that vector is multiplied with sparse unitary matrix $Y$ giving $z = Yx$. Are there any advantages of detecting the sparse vector $x$ ...
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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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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 ...
6 votes
1 answer
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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 \...
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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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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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1 vote
1 answer
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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 $y = h*x$. ...
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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 ...
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1 answer
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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?
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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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1 answer
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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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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 ...
4 votes
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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 ...
5 votes
1 answer
313 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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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-...
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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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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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1 answer
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Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]

This is my implementation which doesn't work: ...
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2 answers
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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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Convex Optimization with $ {L}_{1, 2} $ Regularization Term

I have an optimization problem such as follow: $$\underset{X}{\operatorname{argmin}}\sum _s \left \| T_sX_{:,s} - Y_{:,s} \right \|^2_2 +\lambda\left \| GX \right \|_{2,1} \tag{1}$$ I have introduced ...
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1 answer
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Why Does FISTA Algorithm Not Work for Signed Signals?

Using the FISTA Algorithm for compressive sensing from Tiep H. Vu - FISTA, I created the matlab example below. I created 2 sparse signals x_signed and x_pos, where the latter only contains positive ...
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Resources on Solving Convex Optimization Problems in the Compressed 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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