PTB-MR/mrpro

iterative Sense + Tikonov regularisation

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supersedes #6

Design suggestion for IterativeSENSE reconstruction algorithm

class iterativeSENSE(Reconstruction):
     acquisition_model: LinearOperator
     initial_value: None | IData
     n_max_iterations: int
     dcf: DcfOperator | None

Design suggestion for IterativeSENSEWithTikonov reconstruction algorithm

class iterativeSENSEWithTikonov(Reconstruction):
     acquisition_model: LinearOperator
     initial_value: None | IData
     n_max_iterations: int
     dcf: DcfOperator | None
     regularisation_image: None | IData
     regularisation_weight: float

If regularisation_weight == 0 or regularisation_image is None this defaults to iterativeSENSE

Open questions:

  • Should we have an additional l2_regularised_least_squares optimizer which solves the more general problem ||Ax - y||_2^2 + lambda||Tx - xreg||_2^2 or are we happy to use cg directly
  • In order to be able to write A^H A + lambda as an operator do we need an additional unity operator or can this already be achieved with our current operator classes
  • Would it make sense to have an (Linear)AcquisitionModel Operator which includes the functionality of "from_kdata", "recalculate_csm", "recalculate_fourier_op"... which is currently in DirectReconstruction. DirectReconstruction could then also get acquisition_model as input.

Suggestion: AcquisitionModel is constructed in forward otherwise difficult to handle update of csm, fourier_op...

noise should also be an input