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Questions tagged [variational-methods]

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1 answer
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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 ...
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2 votes
1 answer
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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 ...
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4 votes
1 answer
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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 ...
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5 votes
2 answers
63 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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1 vote
0 answers
37 views

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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6 votes
1 answer
794 views

Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation

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 ...
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