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Questions tagged [compressive-sensing]

the field of study that aims to solve an underdetermined linear system of equations by exploiting the structure of the unknown data

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Significance of $ \lambda $ in Basis Pursuit

In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a $ \lambda $ parameter used as a regularizer. What is its significance?
Gunjan naik's user avatar
14 votes
3 answers
650 views

Is there any alternative characterization of sparsity of a signal in compressed sensing

The starting assumption for compressed sensing (CS) is that the underlying signal is sparse in some basis, e.g., there are a maximum of non-zero Fourier-coefficients for an $s$-sparse signal. And ...
Arnab's user avatar
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12 votes
4 answers
758 views

Universal Bases (Dictionary) for Image Compression

I am a physics graduate student working on a data compression problem. I have been reading Prof. Steven L. Brunton's book on data driven science and engineering. I am fascinated to the concept of ...
Ricky Pang's user avatar
7 votes
2 answers
777 views

Alternative to Orthogonal Matching Pursuit (OMP) Algorithm

In the Compressed Sensing context, assume there is a signal $ x \in {\mathbb{R}}^{n} $ which is $ k $ sparse. Namely its Pseudo $ {\ell}_{0} $ Norm is $ {\left\| x \right\|}_{0} = k $ (The signal has ...
Digi1's user avatar
  • 171
6 votes
3 answers
3k views

Compressive Sensing Incoherence Principle

As people acquainted with Compressive Sensing would know, incoherence and sparsity are two main principles. I've been reading about compressive sampling and developed an interest into the topic. What ...
SimpleMan's user avatar
  • 183
5 votes
1 answer
378 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 ...
Luca Romano's user avatar
5 votes
2 answers
175 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 ...
Maxtron's user avatar
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5 votes
0 answers
188 views

Residual error when setting measurement matrix in compresssive sensing

I have an issue when implementing compressive sensing to recover sparse vector. Assume I have sparse vector $x$ of length, for example, $(256,1)$. $x = [x_1,x_2,.....x_{256}]$. This vector is ...
Gze's user avatar
  • 640
5 votes
1 answer
285 views

Solving LASSO (Basis Pursuit Denoising Form) with LARS

I'm now working on using LARS (Least Angle Regression) algorithm to solve a LASSO problem in Basis Pursuit Denoising form like: \begin{align*} \quad && \arg \min_{\beta}{\left\| y - X\beta \...
queuer's user avatar
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5 votes
1 answer
153 views

On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
Gze's user avatar
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5 votes
2 answers
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Compressive sensing: numerical generation of RIP matrices

The restricted isometry property (RIP) states that: \begin{equation} (1-\delta_K)||x||_2^2 \le ||A x||_2^2 \le (1+\delta_K)||x||_2^2 \end{equation} for any $K$-sparse vector $x$ of length $N$. The ...
gbarr's user avatar
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5 votes
2 answers
181 views

Estimating Convolution Input Under the Assumption of Sparsity and Constant Non Zero Values Using Compressive Sensing Approach

I was wondering about if there is compressive sensing algorithm to estimate the sparse vector where the number of non-zeros values and amplitude of every non-zeros value are known. For example, assume ...
Gze's user avatar
  • 640
4 votes
2 answers
3k views

Iterative Hard Thresholding (Python Implementation) [closed]

I'm trying to implement the Iterative Hard Thresholding recovery algorithm for compressive sensing in python. It is a very simple algorithm, given $ \mathbf{y}( = \mathbf{A}\mathbf{x}), \mathbf{A}$, ...
seeker's user avatar
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4 votes
1 answer
165 views

Resources on Solving Convex Optimization Problems in the Compressed Sensing Field

When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge ...
MJay's user avatar
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3 votes
0 answers
179 views

Compressed Sensing in DOA processing

I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing I use a first FFT to solve the range ...
Luca Romano's user avatar
2 votes
2 answers
641 views

Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
sujit das's user avatar
2 votes
1 answer
432 views

How Come RIP Guarantees Unique Restoration of the Sparse Solution by $ {L}_{1} $ Minimization?

We have a sensing matrix $\Phi$, satisfying the restricted isometry property (RIP), and a sparse signal $x$. We want to recover $\hat x$ from the measurement $y=\Phi x$ by using $l_1$-minimization. I ...
Paul85's user avatar
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2 votes
1 answer
597 views

Calculating an incoherence property from sub-optimal sampling patterns

EDIT (after comments and subject matter review) CS is based on a choice of a sensing basis $\Phi$ relative to a representation basis $\Psi$. Using an "Incoherence Property" $\mu$ that measures the ...
val's user avatar
  • 445
1 vote
1 answer
93 views

Projecting a vector to another to detect the sparse values of such vector

Assuming we have sparse vector of length $N$ such as $X = [0,1,0,-1,0,1,1,0]$ which has some non-zeros values. The vector $x = iFFT(X)$ is convoluted with another vector $h$ resluting $y = h*x$. ...
Gze's user avatar
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