# 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: $$x(t) = \sum_{k=0}^{K} \sum_{n=0}^{N} a_{k,n} \cdot \delta(t - nT_k)$$ ...
60 views

### 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 ...
100 views

### 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 ...
64 views

1 vote
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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 ...
39 views

### 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 ...
1 vote
104 views

### 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. ...
179 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 \...
21 views

### 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 ...
90 views

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

This is my implementation which doesn't work: ...
361 views

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

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
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 ...
258 views

### 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 ...
37 views

### 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 ...
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 ...
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 ...
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 ...
1 vote
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), ...
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 ...
1 vote
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 ...