5 votes
Accepted

How to Solve an Image Deblurring Problem by Variational Methods Using ADMM?

Remark: This is adapted from How to Solve Image Deblurring with Total Variation Prior Using ADMM? Formulation of the Problem I am solving the problem under the following assumptions: The blurring ...
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5 votes
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Variational Regularization Method in Image Processing

This is an example of the Fidelity Term and Prior Term model. In many Inverse Problems we assume some model on the additive noise. This part is modeled by the Fidelity Term ($ \mathcal{D} \left(A \...
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5 votes
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Justification for Squared $ {L}_{2} $ Data and Smoothness Term as an Error Bound

One of the motivations to use the $ {L}_{2} $ norm comes from the Maximum a Posteriori Estimation (MAP) framework. If you model $ \psi \left( u \right) \sim \mathcal{N} \left( 0, \alpha \right) $ ...
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4 votes
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Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation

I'm not sure I fully understood what's the issue you're having. Yet I will show a simple property of the Gaussian filter which might make things clearer. For simplicity, I will use 1D Signal. Yet it ...
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1 vote
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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?

This turned out to be easier than I thought. Image processing is a boundary value problem, and the boundary is the set of pixels along the edge of the image. The common notation for this boundary in ...
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  • 257
1 vote

Justification for Squared $ {L}_{2} $ Data and Smoothness Term as an Error Bound

I figured out how to show that after some time. It's just Jensen's inequality wrt $\|\cdot\|^2_2$ which is a convex function. That is, I first apply the triangle inequality to: $$\|u-g\|_2 = \|(1-\...
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