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of the regularization |

Reconstruction - Regularization |

A simple solution for image restoration = optimizing theleast squarescriterion.

Calculate the image which minimizes the function:J(X)

J(X)=|| Y-HX ||^{2}

This inverse problem is ill-posed(in the sense of Hadamard) :the solution is not unique ; it may be unstable. Reconstructionnoise amplificationSmall variations of the observed image

Yhigh variations of the reconstructed solutionX.

Example (synthetic image) :

Original imageCorrupted imageReconstructed solution

Calculate the image which minimizes the energy :U(X)

=data-dependentterm (Y=data)=

regularizationterm,whichpenalizes noisy solutions, =

hyperparametersof the model

= differences between neighbour pixelsgradients of X=

, it takes into account the constraints imposed on the solutionPhi-function