mr2.algorithms.csm.inati

mr2.algorithms.csm.inati(coil_img: Tensor, smoothing_width: SpatialDimension[int] | int, n_iterations: int = 10) → Tensor[source]

Calculate a coil sensitivity map (csm) using the iterative Inati method [INA2014].

This function computes CSMs using an iterative alternating minimization approach that estimates the combined structural image and the coil sensitivity profiles simultaneously. Compared to covariance-based methods, this approach is more memory-efficient and inherently enforces spatial phase coherence.

The algorithm follows these steps:

  1. Initialize Combined Image: Create an initial coil combination using a global sum of the coil data.

  2. Iterative Refinement: For a specified number of iterations: a. Update the CSMs by dividing the coil images by the combined image and smoothing the results. b. Update the combined image using the newly estimated CSMs (SENSE combination). c. Align the global phase at each step to avoid phase singularities and ensure spatial smoothness.

  3. Final Normalization: Normalize the sensitivity maps to have unit 2-norm across the coil dimension.

This function supports one or more sets of coil images with leading dimensions. The input should be a tensor with dimensions (..., coils, z, y, x). Prefer using CsmData when sensitivity estimation should stay synchronized with MR2 data containers and metadata.

Parameters:

  • coil_img (Tensor) – Images for each coil element, shape (..., coils, z, y, x).

  • smoothing_width (Union[SpatialDimension[int], int]) – Size of the smoothing kernel.

  • n_iterations (int, default: 10) – Number of iterations to refine the maps.

Returns:

csm – Coil sensitivity map, shape (..., coils, z, y, x).

References

[INA2013]

Inati S, Hansen M, Kellman P (2013) A solution to the phase problem in adaptive coil combination. in Proceedings of the 21st Annual Meeting of ISMRM, Salt Lake City, USA, 2672.

[INA2014]

Inati S, Hansen M, Kellman P (2014) A Fast Optimal Method for Coil Sensitivity Estimation and Adaptive Coil Combination for Complex Images. in Proceedings of Joint Annual Meeting ISMRM-ESMRMB, Milan, Italy, 7115.