Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [sparse-model]

24 questions
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Denoising by DCT and hard thresholding

If I have an image and I find the DCT and then apply hard thresholding on the coefficients and then IDCT then I have attenuated the noise. Can someone please explain in detail or point me to the answer as to why this works? I understand why a…
Dino
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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 contaminated such as white gaussian noise, car noise,…
beni
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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 Gaussian prior, it is supposed to be better as it…
feelfree
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Solving a Weighted Basis Pursuit Denoising Problem (BPDN) with MATLAB / CVX

Following up from an answer by @Royi on adding weights to BPDN problem , I would like to use CVX to test this approach. How can we formulate in CVX the regularized LS L1 norm with weights given by a vector $c$, as follows: $$ \arg…
bla
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Adding Variance \ Weights Information When Solving a Basis Pursuit Denoising Problem (BPDN)

Having a "measured" vector $\mathbf{y}$ with its statistics (counts or variance per element), one can use weighted least squares approach to solve the linear system $$\mathbf{A}\mathbf{x} = \mathbf{y}$$ by minimizing $$(\mathbf{y} -…
bla
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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 \right\|}_{2}^{2} + \lambda {\left\| \beta \right\|}_{1} &&…
queuer
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Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code

This is my implementation which doesn't work: function [result,gamma,T]=block_OMP4(phi,signal,N,d,maxIter) [m n]=size(phi); r=signal; gamma=[]; T=[]; i=1; tol=1e-4; err=1; x=zeros(N*d,1); val=[]; figure, while (i<=maxIter && err>tol) maxv=[]; …
sujit das
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4
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2 answers

Constrained LASSO Problem - $ {L}_{1} $ Regularized Least Squares with Linear Equality Constraints

I have an optimization question. I want to solve the following problem: $$ \arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0 $$ in which $\Phi$ is the wavelet transform operator. My strategy is to find the close form…
Z-Harlpet
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custom raw compression

I'm planning to acquire between 50k and 200k image per day with a 50MPixels (or 68MPixels or 130MPixels) sensor; I'll be acquiring the raw data (10 or 12 or 14 bits) from the sensor through SLVS-EC and create a raw file of my own design. The raw…
Soleil
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3
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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 Gaussian noise), would anyone know of a method to infer…
Tom Wenseleers
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Differences Between Two $ {L}_{1} $ Norm Minimization Schemes

I was reading and working with L1 regularized least squares, where: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1} $$ is used to solve for sparse…
dpdp
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Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
sujit das
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2
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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 represetation ? Is a radar received signal sparse or…
Issa
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Sparse Fourier Transform for Sparse Pulse Trains

So I have signals for the form: $$x_{k}(t) = \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ that I receive as a superposition: $$x(t) = \sum_{k=0}^{K} \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ We know that (if we let $N \rightarrow \infty$)…
The Dude
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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 question is how do you determined the maximum value of…
AmandaKamphoff
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