tfmri.recon.sense

sense(kspace, sensitivities, reduction_axis, reduction_factor, rank=None, l2_regularizer=0.0, fast=True)[source]

Reconstructs an MR image using SENSE.

Parameters

  • kspace – A Tensor. The k-space samples. Must have type complex64 or complex128. Must have shape [..., C, *K], where K is the shape of the spatial frequency dimensions, C is the number of coils and ... is the batch shape, which can have any rank. Note that K is the reduced or undersampled shape.

  • sensitivities – A Tensor. The coil sensitivity maps. Must have type complex64 or complex128. Must have shape [..., C, *S], where S is shape of the spatial dimensions, C is the number of coils and ... is the batch shape, which can have any rank and must be broadcastable to the batch shape of kspace.

  • reduction_axis – An int or a list of ints. The reduced axes. This parameter must be provided.

  • reduction_factor –

    An int or a list of ints. The reduction factors corresponding to each reduction axis. The output image will have dimension kspace.shape[ax] * r for each pair ax and r in reduction_axis and reduction_factor. This parameter must be provided.

  • rank –

    An optional int. The rank (in the sense of spatial dimensionality) of this operation. Defaults to kspace.shape.rank - 1. Therefore, if rank is not specified, axis 0 is interpreted to be the coil axis and the remaining dimensions are interpreted to be spatial dimensions. You must specify rank if you intend to provide any batch dimensions in kspace and/or sensitivities.

  • l2_regularizer – An optional float. The L2 regularization factor used when solving the linear least-squares problem. Ignored if fast=False. Defaults to 0.0.

  • fast – An optional bool. Defaults to True. If False, use a numerically robust orthogonal decomposition method to solve the linear least-squares. This algorithm finds the solution even for rank deficient matrices, but is significantly slower. For more details, see tf.linalg.lstsq.

Returns

A Tensor. The reconstructed images. Has the same type as kspace. Has shape [..., S], where ... is the reconstruction batch shape and S is the spatial shape.

Raises

ValueError – If kspace and sensitivities have incompatible batch shapes.

References

1

Pruessmann, K.P., Weiger, M., Scheidegger, M.B. and Boesiger, P. (1999), SENSE: Sensitivity encoding for fast MRI. Magn. Reson. Med., 42: 952-962. https://doi.org/10.1002/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S