# Questions tagged [sparse-model]

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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 ...
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### 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 ...
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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### deconvolution in frequncy vs in time for sparse \ smooth signals

I have a noisy signal $f(t)$ that is measured in time, and I am interested in estimating it's power spectrum, or frequency content. The signal has an impulse response so it can be described as a sum ...
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1 vote
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### how do you know if your matrix is sparse after sparsifying transform?

To successfully compress the data using Compressive Sensing method, I need to have sparse vector, theoretically a vector is sparse if the entries of the vector has many zero or nearly zero. My ...
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### Sparse FFT of ramp using zero padding

I would like to sparsely represent a linear function/ramp in the Fourier domain. In an attempt to improve the sparsity, I have zero padded it. With this padding, it is possible in the example I tried ...
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### Implementation of PCA for hyper-spectral Image Processing

I have been studying the concept of PCA and its implementation for dimensionality reduction for more than 1 month. My goal is to classify a hyperspectral image using sparse representation by the ...
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### Estimate peak width from a vector that is a superposition of unknown number of identical Gaussian peaks with different heights?

If you have a vector that is a superposition of an unknown number of identical Gaussian shaped peaks/impulses of unknown width (but all the same width) and different amplitudes (with Poisson or ...
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### 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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### Compressive Sensing and Sparsity

We apply compressive sensing to reconstruct a signal if it is sparse in the original domain or has a sparse represetation in some basis. How we may know a if a signal is sparse or has a sparse ...
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### Ifft through Matrix multiplication

I am still new to MATLAB, so apologies if I sound lazy to you. I am attempting to model a transformation as a set of matrix operations. I start with a vector, up-sample it by $U$ (up-sampling rate), ...
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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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1 vote
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### When can the impulse response become zero?

The article Efficient Use Of Sparse Adaptive Filters (Proc. Asilomar Conference, Khong et al., 2006) introduces adaptive filters for the estimation of channels or systems having a sparse impulse ...
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### Why Sparse Priors Like Total Variation Opts to Concentrate Derivatives at a Small Number of Pixels?

When performing image deconvolution (deblurring), people often make use of priors to get rid of the illness of the problem. One very common prior is total variation, a sparse prior. Compared to ...
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