mrpro.algorithms.csm.walsh

mrpro.algorithms.csm.walsh(coil_images: Tensor, smoothing_width: SpatialDimension[int] | int) → Tensor[source]

Calculate a coil sensitivity map (csm) using an iterative version of the Walsh method.

This function computes CSMs from a set of complex coil images assuming spatially slowly changing sensitivity maps using Walsh’s method [WAL2000].

The algorithm follows these steps:

  1. Compute Pointwise Covariance: Calculate the covariance matrix of the coil images at each voxel to capture inter-coil signal relationships.

  2. Apply Smoothing Filter: Smooth the covariance matrices across spatial dimensions using a uniform filter of specified width to reduce noise and enforce spatial consistency.

  3. Dominant Eigenvector Estimation via Power Iteration: Perform power iterations to approximate the dominant eigenvector of the covariance matrix at each voxel, representing the principal component of the signal.

  4. Normalize Sensitivity Maps: Normalize the resulting eigenvectors to produce the final CSMs.

This function works on a single set of coil images. The input should be a tensor with dimensions (coils, z, y, x). The output will have the same dimensions. Either apply this function individually to each set of coil images, or see from_idata_walsh which performs this operation on a whole dataset [WAL2000].

This implementation is inspired by ismrmrd-python-tools.

Parameters:

References

[WAL2000] (1,2)

Walsh DO, Gmitro AF, Marcellin MW (2000) Adaptive reconstruction of phased array MR imagery. MRM 43