# 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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### How to improve quality of the recovered image in compressed sensing technology?

I was trying to use compressed sensing technology in image processing. Basically, I did a code in Python(Spyder IDE) which takes an image, compress the image and reconstructs it. I tried with the ...
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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 ...
357 views

### Amplitude and Phase Recovery of a Signal Embedded in Linear Signal with Noise

I have a noisy signal that has an ac component of fixed frequency but variable amplitude and phase. I'd like to recover the ac component. The signal (blue trace) is mostly smooth, but has a few ...
159 views

### Can we use AutoEncoder for Sparse Sensing?

Is there a way to introduce sparsity constraint on an autoencoder to achieve compressions in the Cosine/Fourier domain? I want to use the encoder part of the Auto encoder as the feature extractor from ...
127 views

### Compression Sensing for Blind Source Separation

I am new to Signal Processing, and am interested in compression sensing for audio files. CS is based on the algorithm that, given some sampling of a signal $f$ in order to obtain a smaller (compressed)...
188 views

### Signal Reconstruction in Compressed Sensing with a Simple Vector Signal as an Example

While going through the different types of reconstruction algorithm as mentioned in Richard G. Baraniuk - Compressive Sensing - Lecture Notes (Also on DocDroid), I came to know that minimum ${L}_{1}$...
1 vote
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### Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Does anyone have a reference that specifically discusses choosing the frequency scale for a simple 1D data for non-uniformly sampled time-domain data when performing the discrete Fourier transform. In ...
91 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 ...
23 views

### 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 ...
77 views

### How to build the measurement matrix used for compressive sensing

I have a sparse vector $x \in \mathbb{R}^{N \times 1}$, it's real and positive, the non-zeros values are maximum $N/2$ values. It means, I have at least $N/2$ zeros values in $x$. My question, is it ...
1 vote
144 views

### Sparsity limits of compressed sensing - is this right?

Compressed sensing (CS) guarantees exact object recovery (or with high probability) given a) sufficient measurements are taken in a sparse basis which is b) incoherent vis-a-vis a given object ...
1 vote
2k views

### How to implement compressed sensing reconstruction?

I am new to the field of Compressive Sensing. I'm trying to implement an example in this link. This example have described and implemented a sample tone reconstruction carefully, but unfortunately, ...
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 ...
1 vote
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### 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 ...
2k views

### Compressive sensing: numerical generation of RIP matrices

The restricted isometry property (RIP) states that: $$(1-\delta_K)||x||_2^2 \le ||A x||_2^2 \le (1+\delta_K)||x||_2^2$$ for any $K$-sparse vector $x$ of length $N$. The ...
218 views

### Sub nyquist sampling, required number of samples for time sparse grouped signals

Question: Does it make sense to perform compressed sampling if the non zero samples are grouped in time? If so, what is the minimal length of the vector x that should be acquired to allow full signal ...
386 views

### Why doesn't compressive sensing work for any signal?

My (probably naive) understanding of compressive sensing is that it is a technique that allows to efficiently reconstruct an $N$-dimensional signal $\boldsymbol x$, provided that it is sparse in some ...
1 vote
195 views

### Limited cross-correlation for multiple signals

I have $N$ signals, each of length $\tau$, with $N\ll \tau$, eg. $\tau=10^8$ samples and $N=100$. I want the $r=10$ first components of all pairwise cross-correlation for the $N$ signals. The naive ...
1 vote
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### Discussion "Recovering Low-Rank Matrices From Few Coefficients In Any Basis"

Existing work concentrated mostly on the problem of “matrix completion” where one aims to recover a low-rank matrix from randomly selected matrix elements. Their result covers this situation as a ...
393 views

### Can compressed sensing be used instead of intepolation for missing values?

Consider a signal that is sparse in frequency, but it measured in the time domain, for example (in matlab): ...
183 views

### What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The Fourier basis is a common choice for transformations, but a lot of times, it's not the best for a specific application. For instance, wavelet bases give us better spatial / temporal locality than ...
33 views

### update the image plane distance in Fresnel transform

I have performed reconstruction of images in Fresnel transform using a desired algorithm. Now the aim is to find an optimal value of image plane distance at which the reconstruction is accurate. I ...
23k views

### Compressive Sensing Through MATLAB Codes

I am new to the topic of compressed sensing. I read a few papers about it by R.Baranuik, Y.Eldar, Terence Tao etc. All these papers basically provide the mathematical details behind it, i.e., Sparsity,...
139 views

### Convex Optimization with ${L}_{1, 2}$ Regularization Term

I have an optimization problem such as follow: $$\underset{X}{\operatorname{argmin}}\sum _s \left \| T_sX_{:,s} - Y_{:,s} \right \|^2_2 +\lambda\left \| GX \right \|_{2,1} \tag{1}$$ I have introduced ...
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### Rakeness Optimization problem

Rakeness optimization problem demonstrate that increases the rakeness between $a$ , $b$ while leaving $b$ random enough. where $e$ is the energy of the projection waveforms and $r$ is a randomness-...
254 views

### Clear understanding of compressed sensing

I am trying to get a clear understanding of how compressed sensing works. A continuous signal $x(t)$ is under-sampled (less samples are collected than the numbers required by the Nyquist theorem). The ...
641 views

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

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
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### 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 \...
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### Coherence in compresive sensing

I am starting to write my master thesis, and it's in field of compressive sensing. I have some problems with math behind it. I don't understand the concept of matrix coherence. I know how it is ...
89 views

### 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, ...
1k 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 ...
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 ...
731 views

### Reference Code for Positive Basis Pursuit Denoising

I am trying to reconstruct a positive sparse signal using compressed sensing (friedlanders code), I cannot find a way to impose the positivity constraint for this implementation. I have seen some ...
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### What is an analysis dictionary or operator in compressive sensing?

I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries. Here are some papers that I have read so far: https://www.hindawi.com/...
1 vote
279 views

### Why do we need deterministic measurement matrices in compressed sensing?

I recently introduced myself into the field of CS, but I do not understand why some people try to find deterministic measurement matrices? If I am correct, gaussian random matrices are very powerful ...