To combine multiple diffusion-weighted imaging (DWI) acquisitions while effectively reducing noise and phase cancellations.Diffusion-weighted imaging (DWI) intrinsically suffers from low SNR due to diffusion-induced exponential signal losses. Hence, multiple acquisitions have to be averaged to attain reasonable SNR level in high-spatial-resolution DWI images. However, subject motion during diffusion-sensitizing gradients creates varying phase offsets between repeated acquisitions ¹. Consequently, a direct combination of image repetitions through complex averaging causes phase cancellations and a signal loss. Here, we propose a phase-correcting non-local means denoising filter that combines multiple DWI acquisitions while effectively reducing noise and phase cancellations.

In vivo DWI images of the cervical spinal cord were acquired in the sagittal plane, on a 3T GE MR 750 scanner using 6-channel cervico-thoracic-lumbar (CTL) coil. To achieve high in-plane resolution, the fied-of-view (FOV) in the phase-encode (PE) direction was reduced using a 2D echo-planar RF excitation pulse ^2-5. Single-shot EPI readout with 192x48 imaging matrix, 62.5% partial k-space coverage in the PE direction (i.e., 40 PE lines in EPI readout) were utilized. Diffusion weighting was applied in three orthogonal directions (S/I, A/P, R/L) with $$$ b = 500 \frac{s}{mm^2} $$$ . Other imaging parameters were: 0.9 x 0.9 mm² in-plane resolution, FOV= 18x4.5cm², 4 mm slice thickness, 6 slices, TE = 51.3 ms, TR = 3600 ms, NEX = 16 averages, total scan time of 3 min 52 sec.

K-space data from each slice and each coil were extracted and processed individually with a custom image reconstruction routine implemented in MATLAB. 16 repetitions (NEX) of this data (each with low SNR) were first phase corrected using a refocusing reconstruction ⁶ using the fully-sampled central 12.5% of k-space data. After this preprocessing step, five different reconstruction methods were compared:

a)Each repetition is processed with a POCS algorithm for partial k-space reconstruction ⁷. Absolute value average of the resulting images is taken (Fig. 2a).

b) Image from (a) is denoised via an optimized non-local-means (NLM) filter ^8,9 (Fig. 2b).

c) A complex averaging is performed in k-space, followed by a POCS algorithm for partial k-space reconstruction (Fig. 2c).

d) Image from (c) is denoised via an optimized NLM filter (Fig. 2d).

e) Proposed method: Phase-corrected complex-valued images are processed with a modified NLM filter: 16 repetitions are concatenated in image domain, and the search volume (11x11 pixels) for finding similar neighborhoods (3x3 pixels) is expanded to include the corresponding positions in the repetition images. This modification significantly improves the performance of NLM with minimal increase in reconstruction time. Resulting images are deconcatenated, individually processed by a POCS algorithm for partial k-space reconstruction, and averaged to form the final image. This process is outlined in Fig. 1 and the resulting image is shown in Fig. 2e.

For NLM filters, the tuning parameter that determines the noise vs. resolution trade-off is automatically set using the method described in ⁹, without user intervention.

Figure 2 shows the results of the proposed image reconstruction, in comparison with four alternative techniques. As seen in Fig. 2a, in case of low SNR, absolute value averaging causes an accumulation of noise in the background, which makes it difficult to distinguish low SNR regions in the inferior parts of the cervical spinal cord (blue arrow). A subsequent NLM filter fails to relieve this problem (Fig. 2b). The complex averaged image in Fig. 2c, on the other hand, suffers from signal cancellations (red arrows). Note that these signal cancellations appear despite the prior refocusing algorithm, which can only fix slowly varying phase terms. Local and rapid phase variations on the spinal cord could be a manifestation of the motion around the spinal cord due to CSF pulsation, or oscillatory spinal cord motion synchronized to cardiac cycle ¹⁰. This artifact is especially problematic, as it can be mistaken for an increased diffusion region on the spinal cord. A subsequent NLM filter fails to correct the signal cancellation problem (Fig. 2d). Finally in Fig. 2e, the proposed method does not suffer from signal cancellations, as local phase variations are detected and dealt with using the modified NLM filter. Furthermore, background noise level is significantly reduced, enhancing the depiction of the inferior parts of the cervical spinal cord.We demonstrated a multi-stage image reconstruction algorithm that combines phase correction with a modified non-local-means (NLM) filter performed on complex-valued images. This method visibly improves the image SNR, while avoiding signal cancellations.