Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [sparsity]

The tag has no usage guidance.

-1
votes
1answer
48 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 ...
0
votes
1answer
35 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 ...
3
votes
1answer
71 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 $l_1$-...
1
vote
1answer
59 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 ...
3
votes
2answers
102 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 ...
1
vote
1answer
66 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 ...
2
votes
2answers
76 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 ...
0
votes
2answers
77 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 ...
1
vote
0answers
31 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 ...
1
vote
1answer
33 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} \...
0
votes
1answer
679 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 ...
0
votes
0answers
33 views

In NMF: How to decide which matrix can be applied group sparsity constraint

In simple setting, my signal has specific pattern peak detected at some minutes like in $V$ matrix. I have prior knowledge that $V$ can be mixed from 6 patterns which is belong to 2 groups but cannot ...
0
votes
2answers
142 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 ...
6
votes
2answers
519 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 ...
1
vote
0answers
61 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 ...
8
votes
1answer
1k 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 ...
4
votes
1answer
169 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 ...
0
votes
0answers
63 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 ...
3
votes
1answer
221 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.). ...
3
votes
2answers
209 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\...
0
votes
1answer
84 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 ...
5
votes
1answer
447 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 ...
1
vote
1answer
53 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-...
1
vote
2answers
114 views

Real world application of signal sparsity other than Cognitive Radio?

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 ...
-1
votes
1answer
219 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 ...
1
vote
1answer
334 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 ...
1
vote
1answer
66 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 ...
1
vote
2answers
219 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 ...
0
votes
1answer
95 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 ...
0
votes
2answers
26 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?
0
votes
1answer
87 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 ...
0
votes
0answers
386 views

Multiplying two large sparse matrices

I am having two big large sparse matrices A, B, suppose M=256, ...
1
vote
2answers
504 views

Determining The Sparsity or Density of a Chroma Vector

I have a range of songs where I have took an 'unfolded' chromagram computed from a series of short-term windows. Specifically, for one song, I have one vector which contains the amplitudes of the ...