Questions tagged [sparse-model]

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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: $$x(t) = \sum_{k=0}^{K} \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ ...
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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 ...
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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 ...
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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} = \...
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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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1 answer
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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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2 votes
1 answer
57 views

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\| \...
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Improving Main Lobe Width of FFT

It is common knowledge that the duration time samples are collected is inversely proportional to the width of the main lobe in the Fourier domain. The simple example is the rectangular pulse in time ...
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1 answer
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Is it common to impose the sparsity on the Fourier coefficient itself?

In compressive sensing, I see many works to impose the sparsity on the wavelet coefficients (e.g., by minimizing the L1 norm of such coefficients.) Another example in MRI is to impose sparsity on the ...
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A hypercomplex encoding to preserve spatial/temporal information? [closed]

I have recently come across the idea of encoding a 1D signal (i.e. a mono audio) as a complex vector instead of as a vector of reals, where the imaginary part is used to encode the cells' positions. ...
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6 votes
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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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2 votes
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Solving Sparse Model with given Dictionary Using LASSO

I was trying to solve a problem where the basis matrix contains the components of $\sin(nx)$, $\cos(nx)$, $\sinh(nx)$ and $\cosh(nx)$. Say the $n$ varies from 1 to 100. While solving the lasso linear ...
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5 votes
1 answer
90 views

Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]

This is my implementation which doesn't work: ...
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3 votes
2 answers
361 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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6 votes
1 answer
121 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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2 answers
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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 ...
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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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3 votes
4 answers
423 views

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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7 votes
2 answers
190 views

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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2 votes
2 answers
150 views

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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  • 147
1 vote
2 answers
1k views

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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  • 133
0 votes
2 answers
258 views

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
2 answers
953 views

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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6 votes
1 answer
371 views

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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  • 527
11 votes
3 answers
1k views

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 ...
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