# Tag Info

### Best Metric to Compare Sparsity of Vectors

I am sorry I cannot comment your answer due to my low reputation. Gini and your suggested sparsity ratio ($l_1(x)/l_2(x)$) both give me the same value for $\lambda$. But The problem I still see is ...
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### Compressive Sensing vs. Sparse Coding

As you correctly noted compressed sensing, compressive sampling, sparse sampling all mean the same thing. Some authors also call it sparse sensing. The idea behind compressed sensing is that a sparse ...
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### Why doesn't compressive sensing work for any signal?

You can measure and reconstruct such a 1-sparse signal as you describe in your question. The crucial misunderstanding here is, as @MBaz points out, that you have to know the basis $\Psi$. You can ...
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### Universal Bases (Dictionary) for Image Compression

This is a great and interesting question. There are 2 ways to look at it, empirically and analytically. But before we start, a major detail is that when dealing with images we mainly talk about the ...
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### Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

The main advantage of OMP is that the residual is orthogonal to the current solution. Let's say you select all $k$ columns from $A$ (also called atoms) at once and let us also presume that $A$ is an ...
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### Relationship between information retrieval and source separation in signal processing

There are, a few discrepancies that might be making a difference here. My suggestion would be to edit the question for clarity. There are quite a few assumptions that lead to non-straightforward ...
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### Compressive Sensing vs. Sparse Coding

A couple of reference works offer an exaplanation: A neurological interpretation described in Scholarpedia Stanford's Unsupervised Feature Learning and Deep Learning tutorial If we look at the ...
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### Can compressed sensing be used instead of intepolation for missing values?

Yes, at least in the above case it is possible. Though it might not be computationally as cheap as other methods such as least squares based curve fitting. I do not think injecting NaN gonna help, ...
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### Universal Bases (Dictionary) for Image Compression

As a complement to the neat answer by @Royi, I would add that "sparsity" is originally a heuristic principle in science, that applies well to many interesting really world data and problems. ...
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### Real world application of signal sparsity?

Sparsity concept is extensively being used in computer vision and image processing. The Idea is that natural image can be pretty sparse when it is transformed to different bases. this bases can be ...
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### Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

What you propose is actually being used in other algorithms. Your proposal corresponds to the first step of iterative hard thresholding. After the first step, the residual is updated, correlation ...
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### What are the practical constraints on designing Sensing matrix in compressed Sensing?

Checking for RIP of a matrix is an NP-Hard problem which means it is not computationally feasible to accomplish. RIP is used in matrix design mostly in theoretical aspects. Stealing @David 's comments,...
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### Terminologies - sparse channel, sparse input, compressed sensing

The term sparse, as you mention, refers to the fact that some "signal", usually represented by a vector $x$ contains mostly zero or negligible values and only a few non-zero or significant ...
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### Compressive Sensing with Square Measurement Matrix

It's important to clearly distinguish the terms Compressive Sensing (CS) and Sparse Signal Recovery (SSR). CS is about taking fewer measurements than what classical criteria such as Nyquist would ...
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Well, in your example, the channel isn't exactly sparse. It has been shown that $\ell_0$ minimization can recover any $K$-sparse vector $x$ from observations $\Phi x$ as long as \$2K < {\rm spark}(...