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Module tikhonov

Module tikhonov 

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Tikhonov regularization for QSM

Tikhonov regularization adds an L2 penalty term to stabilize the inversion:

chi = argmin_x ||Dx - f||_2^2 + lambda||Gamma*x||_2^2

This has a closed-form solution in k-space: chi_hat = D* * f_hat / (|D|^2 + lambda|Gamma|^2)

Reference: Bilgic, B., et al. (2014). “Fast image reconstruction with L2-regularization.” Journal of Magnetic Resonance Imaging, 40(1):181-191. https://doi.org/10.1002/jmri.24365

Reference implementation: https://github.com/kamesy/QSM.jl

Structs§

TikhonovParams
Tikhonov algorithm parameters

Enums§

Regularization
Regularization type for Tikhonov

Functions§

tikhonov
Tikhonov regularization for dipole inversion