Due to the intrinsic low signal to noise ratio in diffusion weighted imaging (DWI), magnitude processing often results in an overestimation of the signal’s amplitude. This results in low estimation accuracy of diffusion models and reduced contrast because of a superposition of the image signal and the noise floor [1]. We adopt a new phase correction (PC) technique yielding real valued data and maintaining a Gaussian noise distribution.

Prah et al. suggested the following PC method [2]:

1. Filter the complex DWIs using a boxcar kernel in image space

2. Extract the phase of the filtered DWIs

3. Subtract the phase of the filtered images from the original DWIs.

4. Post-process the real part of the data only.

The disadvantage of this approach is a substantial remaining bias if small filter kernels are used or a high vulnerability to local phase variations if large filter kernels are used. In Fig. 1a a typical EPI processing pipeline is shown including odd-even phase correction (OEC), ramp-sampling (RS) and Partial Fourier (PF). While a inverse discrete Fourier transform (IDFT) is an orthogonal transform, reconstruction of RS or PF data is not. Consequently noise correlation with neighbors in image space is introduced (Fig 1b). Therefor we propose new filter kernels which assign high weights to weakly correlated voxels and low weights to highly correlated voxels ("Opt" kernels, Fig. 1c). If the local phase in a DWI exceeds a certain level of inhomogeneity, the PC becomes corrupted and unwanted signal loss occurs. To detect these errors, we derive a simple thresholding method:

1. Estimate the global noise amplitude σ.

2. Compute the difference maps Δ_MR of the magnitude and real valued images smoothed by a 3×3 boxcar kernel.

3. Detect outliers by thresholding Δ_MR with σ_T=2σ.

4. Replace detected outliers with the magnitude data.

Assuming Gaussian noise, the probability that a voxel with zero true signal randomly exceeds σT is approximately 4% for σ_T=2σ.

DWIs were recorded with matrix sizes of 96×96×17 (ACQ1) and 96×96×11 (ACQ2), and axial-oriented scan volumes of 24×24×4.25 cm³ (ACQ1) and 24×24×2.75 cm³ (ACQ2) covering the brain at the corpus callosum level. Further acquisition parameters were isotropic resolution 2.5 mm, TE=80.7 ms (ACQ1) and 105.1 ms (ACQ2), TR 1800 ms (ACQ1) and TR 1700 ms (ACQ2) and echo spacing 0.592 ms. ACQ1 comprises 10 repetitions of a 3-shell scheme with 25, 35, and 70 directions per shell, and corresponding b-values of 750/1070/3000 mm²/s. ACQ2 comprised 4 repetitions of an 11-cube DSI acquisition scheme with 514 DWIs on a spherically bounded Cartesian grid and a maximum b-value of 8000 mm²/s. Further, we conducted Monte Carlo simulations assuming the same EPI reconstruction chain as being used for the volunteer data.

Fig. 2 presents the Monte Carlo simulation results of the magnitude and real-valued data using different phase filtering kernels. The performance of the filtering kernels well agrees with the amount of remaining noise correlation (Fig. 2a,b). Also the remainning noise floor in ACQ1 well agrees with the simulated results proving that the MR scanner generates near-perfect Gaussian noise and validates the simulation assumptions (Fig. 2b). Fig. 2d-f shows that in the presence of a phase gradient, PC performs very accurately up to a certain value of the phase gradient, after which it immediately breaks down.

Fig. 3 shows the reduction of the noise floor and the increased contrast of PC data compared to magnitude reconstruction for b=3000 s/mm² and 8000 s/mm². However, in cases of very strong local phase variations, PC failes as predicted by the simulations (Fig. 4.). In this case failures of PC can be detected using the tresholding method and the real value is replace by the magnitude (Fig. 4f). Fig. 5 demonstrates the improved delineation of the ensemble average propagator (EAP) when PC is used.

Compared with the method of Prah et al. [2], our novel PC technique significantly reduced the Rician bias, whereas it only slightly increased the sensitivity to local phase variations. Errors in PC were are taken care of in their majority by an outlier estimation technique and the manitude value was used for those voxels. The advantage of PC was shown in a DSI experiment where the EAP was better delineated in the real valued data and delineation improved as the noise floor was lowered. Fiber crossings that were at most barely visible in the EAP of the magnitude data were clearly visible in the real valued data. In conclusion, decorrelated phase filtering seems a very promising technique to improve data quality in DWI.