# Questions tagged [variational-methods]

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### Cross-quantilogram method

What is this method in general? What is the main difference between the quantile cross-spectrum (QS) approach developed by Baruník and Kley (2019) and the cross-correlation function (QS) developed by ...
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Let $f$ and $g$ be two images. With two functions $a$ and $b$ the brightness difference of the images is to be estimated with the following functional $E(a,b) = \int_{\Omega} (((a \cdot f+b)-g)^2 + \... 4 votes 1 answer 454 views ### How to Solve an Image Deblurring Problem by Variational Methods Using ADMM? Following up on a previous question, I wanted to understand how to solve an image deblurring problem using Variational methods in matlab or julia. Given some original blurry image$f$, I would like to ... • 257 2 votes 1 answer 163 views ### Why Does the Rudin Osher Fatemi (ROF) Method Use Variational Methods for Image Denoising When Denoising Problems Are Not Boundary Value Problems? I was reading the recent book Variational Methods in Image Processing by Vese and Guyader which is quite interesting. In the book the authors discuss different types of image processing problems, from ... • 257 3 votes 1 answer 66 views ### Variational Regularization Method in Image Processing I would like to understand better variational regularisation methods in image processing. In particular, the formulas in this image: Why formula (3.13)? In the notes that I read I cannot find ... 4 votes 2 answers 72 views ### Justification for Squared$ {L}_{2} \$ Data and Smoothness Term as an Error Bound

Often in variational methods (and not only) we have an energy that is of the form: $$E(u) = \frac{1}{2}\|f-u\|^2_2 + \frac{\alpha}{2}\|\psi(u)\|^2_2,$$ where the first term is referred to as the data ...
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### Is the behaviour of the following filter plausible?

I've designed a filter based on this equation $$E(u) = \frac{1}{2}\int_{\Omega} \left[(u-f)^2 + g(\lVert \nabla u \rVert)\right]dxdy$$ Euler-Lagrange equations in this case are (should be) given ...
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While I was reading SIFT paper(Lowe, 2004), I came across the method that he apply "heat diffusion equation" to Gaussian function to derive that $$\frac{∂G}{∂σ} = σ∇^2G$$ I searched Wikipedia and ...