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
146
questions
3
votes
0
answers
95
views
Problem about Theorem 3 proof of David L. Donoho's Compressed Sensing
I am dealing with the proof of Theorem 3 of Donoho's paper on compressed sensing. Theorem 3, giving the equilibrium of Gel'fand $n$-width and the optimal error of recontructed signal, is as follows:
...
- 31
2
votes
1
answer
125
views
Compressed sensing and Logan's Theorem
The authors of the book, Data Driven Science & Engineering Book webpage, also have a Youtube Channel. ne of the videos on compressed has the title "Beating Nyquist with Compressed Sensing.&...
- 606
1
vote
0
answers
50
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 ...
- 11
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 ...
1
vote
1
answer
216
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 ...
- 606
4
votes
1
answer
92
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 ...
- 66
0
votes
0
answers
24
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 ...
1
vote
0
answers
37
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 ...
1
vote
1
answer
220
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
25
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
...
- 111
6
votes
3
answers
192
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 ...
- 133
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 ...
3
votes
1
answer
78
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 ...
- 317
12
votes
4
answers
768
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 ...
- 223
9
votes
1
answer
277
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 ...
- 91
0
votes
0
answers
96
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
73
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....
- 317
1
vote
0
answers
140
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 ...
- 111
0
votes
0
answers
69
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 ...
- 33
4
votes
1
answer
763
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), ...
- 135
5
votes
1
answer
172
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 ...
- 61
0
votes
0
answers
49
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, ...
- 101
1
vote
0
answers
162
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 ...
- 61
3
votes
1
answer
90
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, ...
3
votes
1
answer
461
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 ...
- 31
2
votes
0
answers
45
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/...
0
votes
1
answer
49
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 ...
- 457
5
votes
1
answer
388
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 ...
- 125
3
votes
0
answers
182
views
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 ...
- 125
3
votes
2
answers
82
views
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\, |\, ...
- 153
2
votes
1
answer
42
views
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 "...
- 23
1
vote
0
answers
63
views
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 $...
- 11
1
vote
0
answers
89
views
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 ...
- 618
1
vote
0
answers
113
views
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.
...
- 640
2
votes
1
answer
483
views
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 ...
- 133
0
votes
1
answer
281
views
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 $x$ ...
- 640
5
votes
2
answers
185
views
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 ...
- 640
0
votes
1
answer
170
views
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 ...
- 75
5
votes
1
answer
303
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 \...
- 53
5
votes
0
answers
189
views
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 ...
- 640
5
votes
1
answer
157
views
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 ...
- 640
1
vote
1
answer
97
views
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 $y = h*x$. ...
- 640
0
votes
1
answer
207
views
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 ...
- 640
2
votes
1
answer
147
views
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?
- 75
2
votes
1
answer
39
views
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 = \...
- 311
5
votes
1
answer
416
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):
...
- 588
0
votes
0
answers
144
views
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 ...
- 59
5
votes
0
answers
77
views
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 ...
- 183
4
votes
1
answer
512
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 ...
- 63
3
votes
0
answers
37
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-...
- 59