mrpro.algorithms.reconstruction.IterativeSENSEReconstruction

class mrpro.algorithms.reconstruction.IterativeSENSEReconstruction[source]

Bases: RegularizedIterativeSENSEReconstruction

Iterative SENSE reconstruction.

This algorithm solves the problem \(\min_{x} \frac{1}{2}||W^\frac{1}{2} (Ax - y)||_2^2\) by using a conjugate gradient algorithm to solve \(H x = b\) with \(H = A^H W A\) and \(b = A^H W y\) where \(A\) is the acquisition model (coil sensitivity maps, Fourier operator, k-space sampling), \(y\) is the acquired k-space data and \(W\) describes the density compensation [PRU2001] .

Note: In [PRU2001] a k-space filter is applied as a final step to null all k-space values outside the k-space coverage. This is not done here.

[PRU2001] (1,2)

Pruessmann K, Weiger M, Boernert P, and Boesiger P (2001), Advances in sensitivity encoding with arbitrary k-space trajectories. MRI 46, 638-651. https://doi.org/10.1002/mrm.1241

Initialize IterativeSENSEReconstruction.

For a regularized version of the iterative SENSE algorithm please see RegularizedIterativeSENSEReconstruction.

Parameters:

kdata (KData | None, default: None) – 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) – Noise 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.
n_iterations (int, default: 5) – Number of CG iterations

Raises:

ValueError – If the kdata and fourier_op are None or if csm is a Callable but kdata is None.

n_iterations: int: Number of CG iterations.

regularization_data: torch.Tensor: Regularization data (i.e. prior) \(x_0\).

regularization_weight: torch.Tensor: Strength of the regularization \(\lambda\).

regularization_op: LinearOperator: Linear operator \(B\) applied to the current estimate in the regularization term.

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.