# Questions tagged [sparsity]

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### 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 ...
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 ...
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### 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
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 ...
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 ...
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1 vote
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### 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 ...
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### 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 ...
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1 vote
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### 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, ...
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 ...
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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 ...
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### 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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### 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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### 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
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 ...
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### 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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### 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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### 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 ...
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### 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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### 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 ...
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### 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 ...
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1 vote
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### 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 ...
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1 vote
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 ...
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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 ...
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### 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 ...