Questions tagged [total-variation]

23 questions
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Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions

I know this is signal dependent, but when facing a new noisy signal what is your bag of tricks for trying to denoise a signal while maintaining sharp transitions (e.g. so any sort of simple averaging, i.e. convolving with a gaussian, is out). I…
John Robertson
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Image Denoising with Better Edge Preservation

I have the input image : and the output of vein detection for the leaf using a Gabor filter, but the output is really noisy: I tried using Total variation denoising however the results are not good: However I don't want to loose the fine details…
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How Can I Use MATLAB to Solve a Total Variation Denoising / Deblurring Problem?

The Total Variation Denoising Problem is given by: $$ \arg \min_{x} \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right) $$ Where $ \operatorname{TV} \left( \cdot \right) $ is the Total Variation Norm. How…
7
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1 answer

Gradient of Total Variation of Magnitude of Complex Function for Denoising

Say I have a complex function $f^*$ (e.g. a MRI image) that has a near piece-wise constant magnitude, but a non constant phase. If I have an optimization problem to find $f^*$ and set up an objective function with a total variation term (e.g. for…
7
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3 answers

Using Total Variation Denoising to Clean Accelerometer Data

I know this is maybe a very basic question but I am doing this as a hobby and I can't find a solution to this problem. Basically I am trying to remove some noise from data I am reading from an accelerometer. This is what I want to achieve (Taken…
Andres
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6
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Solve Efficiently the 1D Total Variation Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with Total Variation Regularization? I know gradient based methods, I wonder how much faster / efficient I can get.
6
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1 answer

How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM?

How could one use the Total Variation frame work to solve the Deblurring problem? Specifically using the ADMM as a solver. One could assume the blurring operator is known, linear and shift invariant. What are the advantages of the TV approach? What…
6
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2 answers

How to Solve Image Denoising with Total Variation Prior Using ADMM?

I was looking at some articles or Wikipedia on denoising images using the Total Variation norm. The setup is the Rudin Osher Fatemi (ROF) scheme, and the corresponding equation is: $$ F(u)=\int_{\Omega}|D u|+\lambda \int_{\Omega}(K u-f)^{2} d…
6
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3 answers

Deconvolution of a 1D Time Domain Wave Signal Convolved with Series of Rect Signals

I have a synthesized signal (the bottom of the following figure), which is the convolution of the input signal (at the top) and the objective function (in the middle). The intention is to retrieve the objective function from the convoluted signal,…
6
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1 answer

The Meaning of the Terms Isotropic and Anisotropic in the Total Variation Framework

The isotropic TV is defined as the estimation of 2-norm of gradients $\sqrt{(y_{i+1,j}-y_{i,j})^2+(y_{i,j+1}-y_{i,j})^2}$, while the anisotropic TV is defined as the estimation of 1-norm of gradients $|y_{i+1,j}-y_{i,j}|+|y_{i,j+1}-y_{i,j}|$. Now I…
4
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1 answer

How to Solve Blind Image Deblurring with Total Variation (TV) Prior Using ADMM?

As a continuation of the question How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM? I would like to understand how could one solve the Blind Deblurring (Deconvolution) problem given that the blurring operator is linear…
4
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How to Solve an Image Deblurring Problem by Variational Methods Using ADMM?

Following up on a previous question, I wanted to understand how to solve an image deblurring problem using Variational methods in matlab or julia. Given some original blurry image $f$, I would like to find the deblurred version $u$. $K$ is a…
4
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1 answer

How to solve ADMM for TV Minimization Problem For Different Sizes $A$ and $x$ in $Ax=b$

I have matrix $A$ that is $(M \times M)$ square matrix, $x$ $(M \times N)$ matrix, $b$ is $(M \times N)$ matrix. Knowing $A$ and $b$ I would like to get the $x$ from the equation $Ax=b$. $N=p \times q$, so consider $x$ as an $M$ number of $p \times…
4
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1 answer

What Does the Total Variation Norm Mean in the Context of Image Processing

What is the notion of total variation and how is total variation norm calculated in an image? More exactly, I want to calculate and understand the meaning of $ \left \|X \right \|_{TV} $ if $X$ is an image. If I optimize: $$ min_{X} \left \|X…
M.Jalali
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Is the Bilateral Filter a Solution of Some Variational Method?

I've been watching these video lectures about variational methods in computer vision. In one of such video lectures a it is explained for example that the Gaussian filtering is a solution of the diffuse equation (so Gaussian filtering is a specific…
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