mr2.algorithms.prewhiten_kspace

mr2.algorithms.prewhiten_kspace(kdata: KData, knoise: KNoise, scale_factor: float | Tensor = 1.0) → KData[source]

Calculate noise prewhitening matrix and decorrelate coils.

Steps:

  • Calculate noise correlation matrix \(N\).

  • Carry out Cholesky decomposition \(L L^H = N\).

  • Estimate noise decorrelation matrix \(D = L^{-1}\).

  • Apply \(D\) to k-space data.

More information can be found in [ISMa] [HAN2014] [ROE1990].

If the noise data has more samples in the ‘other’-dimensions (batch/slice/…), the covariance matrix is calculated independently for each sample in these dimensions. Singleton leading dimensions in knoise are broadcast over matching dimensions in kdata.

Parameters:

  • kdata (KData) – K-space data.

  • knoise (KNoise) – Noise measurements.

  • scale_factor (float | Tensor, default: 1.0) – Square root is applied on the noise covariance matrix. Used to adjust for effective noise bandwidth and difference in sampling rate between noise calibration and actual measurement: scale_factor = (T_acq_dwell/T_noise_dwell)*NoiseReceiverBandwidthRatio

Returns:

Prewhitened copy of k-space data.

References

[HAN2014]

Hansen M, Kellman P (2014) Image reconstruction: An overview for clinicians. JMRI 41(3) https://doi.org/10.1002/jmri.24687

[ROE1990]

Roemer P, Mueller O (1990) The NMR phased array. MRM 16(2) https://doi.org/10.1002/mrm.1910160203