mrpro.algorithms.reconstruction.TotalVariationRegularizedReconstruction

class mrpro.algorithms.reconstruction.TotalVariationRegularizedReconstruction[source]

Bases: DirectReconstruction

TV-regularized reconstruction.

This algorithm solves the problem \(min_x \frac{1}{2}||Ax - y||_2^2 + \sum_i l_i ||\nabla_i x||_1\) by using the PDHG-algorithm. \(A\) is the acquisition model (coil sensitivity maps, Fourier operator, k-space sampling), \(y\) is the acquired k-space data, \(l_i\) are the strengths of the regularization along the different dimensions and \(\nabla_i\) is the finite difference operator applied to \(x\) along different dimensions \(i\).

__init__(kdata: KData | None = None, fourier_op: LinearOperator | None = None, csm: Callable | CsmData | None = CsmData.from_idata_walsh, noise: KNoise | None = None, dcf: DcfData | None = None, *, max_iterations: int = 100, tolerance: float = 0, regularization_dim: Sequence[int], regularization_weight: float | Sequence[float] | Sequence[Tensor]) → None[source]

Initialize TotalVariationRegularizedReconstruction.

Parameters:

  • kdata (KData | None, default: None) – KData. If kdata is provided and fourier_op or dcf are None, then fourier_op and dcf are estimated based on kdata. Otherwise fourier_op and dcf are used as provided.

  • fourier_op (LinearOperator | None, default: None) – Instance of the FourierOp used for reconstruction. If None, set up based on kdata.

  • csm (Callable | CsmData | None, default: CsmData.from_idata_walsh) – Sensitivity maps for coil combination. If None, no coil combination is carried out, i.e. images for each coil are returned. If a Callable is provided, coil images are reconstructed using the adjoint of the FourierOp (including density compensation) and then sensitivity maps are calculated using the Callable. For this, kdata needs also to be provided. For examples have a look at the mrpro.data.CsmData class e.g. from_idata_walsh or from_idata_inati.

  • noise (KNoise | None, default: None) – KNoise used for prewhitening. If None, no prewhitening is performed

  • dcf (DcfData | None, default: None) – K-space sampling density compensation. If None, set up based on kdata. The dcf is only used to calculate a starting estimate for PDHG.

  • max_iterations (int, default: 100) – Maximum number of PDHG iterations

  • tolerance (float, default: 0) – Tolerance of PDHG for relative change of the primal solution; if zero, max_iterations of PDHG are run.

  • regularization_dim (Sequence[int]) – Dimensions along which the total variation reguarization is applied (\(i\)).

  • regularization_weight (float | Sequence[float] | Sequence[Tensor]) – Strengths of the regularization (\(l_i\)). If a single values is given, it is applied to all dimensions. If a sequence is given, it must have the same length as regularization_dim.

Raises:
max_iterations: int

Maximum number of PDHG iterations.

tolerance: float

Tolerance of PDHG for relative change of the primal solution.

regularization_dim: Sequence[int]

Dimensions along which the total variation reguarization is applied \(i\).

regularization_weight: torch.Tensor

Strengths of the regularization along different dimensions \(l_i\).

dcf: DcfData | None

Density Compensation Data.

csm: CsmData | None

Coil Sensitivity Data.

noise: KNoise | None

Noise Data used for prewhitening.

fourier_op: LinearOperator

Fourier Operator.

__call__(kdata: KData) → IData[source]

Apply the reconstruction.

forward(kdata: KData) → IData[source]

Apply the reconstruction.

Parameters:

kdata (KData) – k-space data to reconstruct.

Returns:

the reconstruced image.

direct_reconstruction(kdata: KData) → IData[source]

Direct reconstruction of the MR acquisition.

Here we use \(S^H F^H W\) to calculate the image data using the coil sensitivity operator \(S\), the Fourier operator \(F\), and the density compensation operator \(W\). \(S\) and \(W\) are optional: If they have not been set in this instance, no coil combination or density compensation, respectively, will be performed.

Parameters:

kdata (KData) – k-space data

Returns:

image data

recalculate_csm(kdata: KData, csm_calculation: Callable[[IData], CsmData] = CsmData.from_idata_walsh, noise: KNoise | None | Literal[False] = None) → Self[source]

Update (in place) the CSM from KData.

Parameters:

  • kdata (KData) – k-space data used for adjoint reconstruction (including DCF-weighting if available), which is then used for CSM estimation.

  • csm_calculation (Callable[[IData], CsmData], default: CsmData.from_idata_walsh) – Function to calculate csm expecting idata as input and returning csmdata. For examples have a look at the CsmData.

  • noise (Union[KNoise, None, Literal[False]], default: None) – Noise measurement for prewhitening. If None, self.noise (if previously set) is used. If False, no prewithening is performed even if self.noise is set. Use this if the kdata is already prewhitened.

recalculate_fourierop(kdata: KData) → Self[source]

Update (in place) the Fourier Operator, e.g. for a new trajectory.

Also recalculates the DCF.

Parameters:

kdata (KData) – k-space data to determine trajectory and recon/encoding matrix from.