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Questions tagged [sparsity]

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30 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 ...
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13 views

Sparse recovery for hyper spectral image classification

I am working on my master thesis which is a classification task and I aim to use sparse recovery technique. I am trying to implement several methods to recover the corresponding coefficient. The ...
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1answer
65 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 $l_1$-...
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1answer
55 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 ...
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Blind Signal Separation for Sparse Signals / Sources

Assume we have $N$ measurements $z_1, ..., z_N \in \mathbb{R}^{n_z} $ that generated by $$ z_i = M v_i + e_i $$ where $v_i \in \mathbb{R}^{n_v}$, $n_v < n_z$ and $e_i$ an error sampled from ...
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Blind Signal Separation for Sparse Signals

Assume we have $N$ measurements $z_1, z_2, \dots, z_N \in \mathbb{R}^{n_z}$ that are generated by $$ z_i = M v_i + e_i $$ where $v_i \in \mathbb{R}^{n_v}$, $n_v < n_z$ and $e_i \in \mathbb{R}^{...
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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 ...
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1answer
61 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 ...
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2answers
75 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 ...
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2answers
66 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 ...
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0answers
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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 ...
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1answer
31 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} \...
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1answer
399 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 ...
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0answers
31 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 ...
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2answers
134 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 ...
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0answers
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what is the difference between GOMP and BOMP?

Both group orthogonal matching pursuit (GOMP) and block orthogonal matching pursuit (BOMP) exploit the block sparsity to recover the signal. Is there any difference between these two algorithms?
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2answers
456 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 ...
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0answers
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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 ...
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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 ...
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1answer
121 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 ...
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60 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
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1answer
193 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.). ...
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2answers
196 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\...
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1answer
80 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
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1answer
401 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
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1answer
51 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-...
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2answers
108 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 ...
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1answer
215 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
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1answer
288 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
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1answer
52 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 ...
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2answers
209 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 ...
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1answer
93 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 ...
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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
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1answer
82 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 ...
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0answers
360 views

Multiplying two large sparse matrices

I am having two big large sparse matrices A, B, suppose M=256, ...
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2answers
484 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 ...