Skip to main content

Questions tagged [sparsity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
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 ...
BENZATER hadj's user avatar
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 ...
Con's user avatar
  • 66
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 ...
shashank ranjan's user avatar
1 vote
0 answers
34 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 ...
Waqeeb Sayeed's user avatar
0 votes
1 answer
119 views

Is there a formal definition of what it means for a signal to be sparse?

Up to now I've never found a rigorous or a formal definition of what it means for a signal to be sparse other than it means that it has a relatively low number of non-zero entries or that the ...
Nyquist-er's user avatar
1 vote
0 answers
28 views

What are the modes of a transform basis?

So, I'm reading Steven Brunton's book, "Data Driven Science & Engineering", and I'm trying to understand what he means by mode in this following excerpt: Most natural signals, such as ...
Nyquist-er's user avatar
0 votes
0 answers
60 views

Reducing or removing autocorrelation in spatially correlated data

I am trying to figure out how one can reduce or preferably remove autocorrelation in spatially correlated data. Using the R code below, one generates spatially correlated data that is normally ...
Show's user avatar
  • 1
1 vote
0 answers
61 views

Parameter choice rules for L1 regularization?

I am solving an L1 regularized least squares of the form like: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \...
yourds's user avatar
  • 123
1 vote
1 answer
436 views

Does BM3D really need the noise power spectrum beforehand?

I'm at the moment trying to implement a neural network which uses BM3D as a preprocessing step. The problem is, when using the python implementation of BM3D from the paper Collaborative Filtering of ...
Gabriel Oliveira's user avatar
1 vote
2 answers
212 views

How to objectively measure how "good" a time-frequency representation of music is?

I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal ...
Sevag's user avatar
  • 205
5 votes
1 answer
136 views

Differences Between Two $ {L}_{1} $ Norm Minimization Schemes

I was reading and working with L1 regularized least squares, where: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \...
dpdp's user avatar
  • 123
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, ...
Ahmed Mokhtar's user avatar
3 votes
1 answer
443 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 ...
blerner's user avatar
  • 31
5 votes
1 answer
384 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 ...
Luca Romano's user avatar
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 $...
Canberk's user avatar
  • 11
1 vote
0 answers
88 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 ...
Fatima_Ali's user avatar
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 ...
Gze's user avatar
  • 640
1 vote
1 answer
26 views

How can I implement Guided Random algorithm walker matrices?

My Question is related to the implementation of the paper Segmentation by retrieval with guided random walks: Application to left ventricle segmentation in MRI After careful reading of the code of the ...
Bilal's user avatar
  • 167
5 votes
1 answer
140 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 ...
strahd's user avatar
  • 169
1 vote
0 answers
197 views

Sparse Bayesian Learning Algorithm in Python - MSE vs. SNR

I am implementing SBL in python. I have plotted a graph between MSE (mean squared error) and SNR (Signal to Noise ratio) The graph must be decreasing, but mine is decreasing till the SNR is negative. ...
ar khunteta's user avatar
-1 votes
1 answer
249 views

Signal Denoising Uniformly in Frequency Domain

I have a noisy sparse signal containing number of frequency components. Is there any method to uniformly denoise this signal. in other words, a method that estimated and eliminates the noise power ...
Ahmad's user avatar
  • 113
0 votes
1 answer
135 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 ...
ffff's user avatar
  • 1
4 votes
1 answer
1k 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 $l_1$-...
Jan's user avatar
  • 189
3 votes
1 answer
200 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 ...
Fatima_Ali's user avatar
6 votes
2 answers
329 views

Is There a Sparse Representation for Noise?

Is there sparse representation for stationary noise and nonstationary noise? How can I learn dictionary for each noise class? (my mean of noise is noises with which speech signals are often ...
beni's user avatar
  • 61
4 votes
1 answer
148 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 ...
Issa's user avatar
  • 127
5 votes
2 answers
177 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 ...
Maxtron's user avatar
  • 396
4 votes
2 answers
3k views

Solving LASSO ($ {L}_{1} $ Regularized Least Squares) with Gradient Descent

To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods. I was wondering however, if the LASSO ...
Effesian's user avatar
1 vote
0 answers
46 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 ...
Digi1's user avatar
  • 171
1 vote
1 answer
47 views

Is sparsity induced penalty in source separation "Entrywise matrix norms"?

I am reading this paper where they introduce norm penalties for source separation. In table 1, the $\log/ l_1$ type is $\sum_{g} log(\epsilon + \lVert H_{g} \rVert_1)$. I wonder this $\lVert H_{g} \...
Jan's user avatar
  • 189
2 votes
1 answer
10k views

What exactly is "sparse representation"? [closed]

I saw a recommended topic for the final project in my university called "dsp and dip applications using sparse representation techniques (MATLAB, C, C++)". I consider taking this topic as my final ...
agelosnm's user avatar
0 votes
2 answers
332 views

How to make the impulse response sparse? How does one know that the channel is sparse?

I am new to sparse channel estimation algorithms and reading research articles. One such paper is blind sparse channel estimation using a modification of the BOMP technique titled, "Blind Acoustic ...
Ria George's user avatar
9 votes
2 answers
2k 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 ...
Learn_and_Share's user avatar
1 vote
0 answers
81 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 ...
Digi1's user avatar
  • 171
13 votes
1 answer
5k views

What is an exact measure of sparsity?

I am currently working on compressed sensing and sparse representation of signals, specificly images. I am frequently asked "what is sparsity definition?". I answer "if most elements of a signal are ...
MJay's user avatar
  • 477
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 ...
SKM's user avatar
  • 621
0 votes
0 answers
76 views

Probability of a random signal being approximately sparse

Given a random signal of length $N$, is there any way of estimating (or bounding) the probability of it having an approximately sparse DFT representation, with the degree of sparseness given by ...
Television's user avatar
2 votes
1 answer
449 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.). ...
Xavier's user avatar
  • 23
5 votes
2 answers
1k 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}^{\ast} = \arg \min_{x} \left\{ \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda ...
Tatackola's user avatar
0 votes
1 answer
345 views

How to prepare and plot unequally spaced, irregular data to a contour plot or similar with MATLAB

I've got a data set of hot-wire measurement velocity amplitudes at a given frequency bin (time data that has already been transformed to the frequency domain and I am just considering data for a given ...
phw's user avatar
  • 1
6 votes
1 answer
858 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 ...
syeh_106's user avatar
  • 223
1 vote
1 answer
77 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-...
Gustavo Higuchi's user avatar
3 votes
3 answers
384 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 ...
MimSaad's user avatar
  • 1,976
-1 votes
1 answer
414 views

Sparse Signal fitting in MATLAB, for a sinusoidal function with more than 8 terms?

I'm trying to fit some data belong to a sum of sines function (Fourier sparse) in MATLAB, however, the number of terms of sine function in MATLAB is limited,i.e. to $1 \leq n \leq 8$. However, I want ...
MimSaad's user avatar
  • 1,976
1 vote
1 answer
472 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 ...
zahra's user avatar
  • 13
1 vote
1 answer
476 views

Can Sparse Fourier transform be used for sparse signal in other domain

I've read that sparse fast Fourier transform can be used to compute the Fourier transform of a signal that is sparse in frequency domain much faster compared to FFT. My question is that can SFFT be ...
Nan's user avatar
  • 123
2 votes
2 answers
508 views

sparse representation for image denoising

When I read papers on image denoising, I always encounter sparse representation. For image denoising, we try to separate image signal from noise. It is assumed that signal is correlated and noise is ...
Jogging Song's user avatar
0 votes
1 answer
172 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 ...
Rashwan's user avatar
0 votes
2 answers
31 views

Is there any transformation to exploit the sparsity of a Gaussian Wave?

I am looking for a transformation in which the gaussian wave when transformed with a particular analysis function would make the energy contents be mostly present only in a short band of frequencies?
Sai dheeraj N's user avatar
0 votes
1 answer
186 views

Question about vanishing moments in wavelet transforms

I am reading the book Noise reduction by wavelet thresholding by Maarten Jansen. About vanishing moments, it reads To create a really sparse representation, we try to make coefficients that live ...
Jogging Song's user avatar