Skip to main content

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
43 views

How to improve quality of the recovered image in compressed sensing technology?

I was trying to use compressed sensing technology in image processing. Basically, I did a code in Python(Spyder IDE) which takes an image, compress the image and reconstructs it. I tried with the ...
0 votes
0 answers
15 views

What is the support detection probability after sparse recovery using OMP and Random sampling

I am working on Compressive spectrum sensing CSS. I performed random sampling, OMP recovery. The detection is done by finding nonzero amplitudes in the recovered spectrum to decide the belonging of ...
3 votes
1 answer
357 views

Amplitude and Phase Recovery of a Signal Embedded in Linear Signal with Noise

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 ...
5 votes
1 answer
159 views

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 ...
5 votes
1 answer
127 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)...
6 votes
1 answer
188 views

Signal Reconstruction in Compressed Sensing with a Simple Vector Signal as an Example

While going through the different types of reconstruction algorithm as mentioned in Richard G. Baraniuk - Compressive Sensing - Lecture Notes (Also on DocDroid), I came to know that minimum $ {L}_{1} $...
1 vote
1 answer
196 views

Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Does anyone have a reference that specifically discusses choosing the frequency scale for a simple 1D data for non-uniformly sampled time-domain data when performing the discrete Fourier transform. In ...
4 votes
1 answer
91 views

Room Impulse Response Domain of Sparsity

I have been studying the problem of room impulse responses (RIRs) interpolation for a couple of months. I am trying to use compressed sensing to reconstruct (at best) the sound field in the room with ...
0 votes
0 answers
23 views

How to know which type of sensing matrix would do the job?

Compressed sensing refers to the recovery of a high-dimensional but sparse vector $x\in\mathbb{R}^n$ from its linear measurement $y = Ax+\eta$, where $A\in\mathbb{R}^{m\times n}$ $(m<<n)$ is a ...
3 votes
1 answer
77 views

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 ...
1 vote
0 answers
144 views

Sparsity limits of compressed sensing - is this right?

Compressed sensing (CS) guarantees exact object recovery (or with high probability) given a) sufficient measurements are taken in a sparse basis which is b) incoherent vis-a-vis a given object ...
1 vote
1 answer
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, ...
12 votes
4 answers
758 views

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 ...
1 vote
0 answers
30 views

Spark of the array manifold of a random antenna array

let's consider I have an antenna array with N-elements, and its sensors are not placed in a uniform linear array fashion (may be randomly placed, a coprime array, or a nested array, for example). What ...
5 votes
2 answers
2k 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 ...
3 votes
1 answer
218 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 ...
6 votes
1 answer
386 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 ...
1 vote
1 answer
195 views

Limited cross-correlation for multiple signals

I have $N$ signals, each of length $\tau$, with $N\ll \tau$, eg. $\tau=10^8$ samples and $N=100$. I want the $r=10$ first components of all pairwise cross-correlation for the $N$ signals. The naive ...
1 vote
0 answers
23 views

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 ...
5 votes
1 answer
393 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): ...
6 votes
3 answers
183 views

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 ...
2 votes
0 answers
33 views

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 ...
14 votes
6 answers
23k views

Compressive Sensing Through MATLAB Codes

I am new to the topic of compressed sensing. I read a few papers about it by R.Baranuik, Y.Eldar, Terence Tao etc. All these papers basically provide the mathematical details behind it, i.e., Sparsity,...
5 votes
1 answer
139 views

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 ...
3 votes
0 answers
36 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-...
9 votes
1 answer
254 views

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 ...
2 votes
2 answers
641 views

Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
5 votes
1 answer
285 views

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 \...
0 votes
0 answers
76 views

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 ...
3 votes
1 answer
89 views

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, ...
6 votes
1 answer
1k 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 ...
5 votes
2 answers
175 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
6 votes
2 answers
731 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 ...
3 votes
1 answer
70 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....
1 vote
0 answers
134 views

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 ...
19 votes
4 answers
992 views

Applicability of compressed sensing / compressive sensing

From what I have heard, compressed sensing can only be utilized for a sparse signal. Is this correct? If that is the case, how can a sparse signal be distinguished from any bandlimited signal? Every ...
4 votes
1 answer
747 views

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), ...
0 votes
0 answers
68 views

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 ...
0 votes
0 answers
47 views

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, ...
2 votes
1 answer
467 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 ...
4 votes
1 answer
165 views

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 ...
1 vote
0 answers
160 views

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 ...
5 votes
1 answer
398 views

Compressive Sensing: What Class of Signals Are Exactly Model Sparse?

In traditional compressed sensing, one would require $ m = O ( K.logN)$ measurements to recover a signal of size $N$, and sparsity $K$. The paper, Richard Baraniuk - Model Based Compressive Sensing, ...
4 votes
1 answer
153 views

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 ...
3 votes
1 answer
426 views

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 ...
2 votes
2 answers
293 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 ...
2 votes
0 answers
44 views

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/...
1 vote
2 answers
279 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 ...
5 votes
1 answer
378 views

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 ...
0 votes
1 answer
47 views

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 ...