While multi-spectral imaging sequences, such as MAVRIC-SL, have proven effective at imaging near metallic implants, they often suffer from blurring in the frequency-encode direction due to varying shift in neighboring spectral bins. A deblurring scheme has been proposed that uses a field-map estimate to correct this effect, but it may add distortion as well as noise from spectral bins that do not contain real signal [1]. While the field-map can be estimated from the MAVRIC-SL data itself, current techniques become biased in the presence of noise. Here we propose a new field-map estimation scheme, using an SNR-optimal matched filter approach, and a new bin combination method that removes blurring, artifacts, and noise arising from spectral bins that do not contain real signal.

Current field-map estimation uses a center-of-mass technique given as$$f_{CM}(x,y,z)=\frac{\sum_1^{N_b}s_b(x,y,z)f_b}{\sum_1^{N_b}s_b(x,y,z)},$$ where$$$\:N_b\:$$$is the number of spectral bins acquired,$$$\:f_b\:$$$is the excitation center frequency of bin$$$\:b,\:$$$and$$$\:s_b\:$$$is the magnitude bin signal at the given pixel. While this method works well in the absence of noise, it is very sensitive to noise and becomes biased towards the center bin when using magnitude images.

Matched filters are SNR-optimal linear detectors in the presence of Gaussian noise and are not prone to bias. For MSI, this is accomplished by comparing the magnitude signal across bins with the signal variations that would be expected at different frequencies. This matched filter field-map estimate is then$$f_{MF}(x,y,z)=\text{argmax}_{f}\:s_{mf}(x,y,z,f),\:\text{and}\:s_{mf}=\sum_1^{N_b}s_b(x+\frac{f-f_b}{BW_p},y,z)RF(f-f_b),$$where$$$\: s_{mf}(x,y,z,f)\:$$$represents the matched filter signal,$$$\:RF\:$$$is the rf-profile used to excite the bins,$$$\:BW_p\:$$$is the readout bandwidth per pixel, and$$$\:\frac{f-f_b}{BW_p}\:$$$accounts for the varying spatial shift between bins. Figure 1 shows the center-of-mass and matched filter field-map estimates of an example spectral bin profile with and without noise.

Instead of combining bins by taking the root-sum-of-squares (RSOS) across all bins, as is commonly done, noise can be suppressed by using the matched filter signal$$$\: s_{mf}(x,y,z,f_{MF}),\:$$$which only adds signal from bins that are expected to have it. As field-map estimation error leads to distortion and edge artifacts, a goodness-of-fit metric, a value ranging from 0 to 1 indicating the similarity between the actual and expected bin signal profile, is used to account for situations when the field-map estimate is not reliable. Using the goodness-of-fit, the final image is a weighted average of the RSOS image, which has blurring but no distortion, with the deblurred image, which may have distortion when the field-map is inaccurate. Our proposed reconstruction pipeline is shown in Figure 2.

For validation of the proposed techniques, a digital hip implant phantom was created with realistic off-resonance maps. A 3D MAVRIC-SL scan was then simulated, followed by adding complex Gaussian noise with SNR=40 before taking the image magnitude.

This method was also validated in an agar phantom with a hip implant and resolution grid. The phantom scan parameters were: TE/TR=7.4/4000ms, matrix-size=512x384x40, FOV=30x30x8cm$$$^3,\:$$$and acquisition-time=35 minutes. A volunteer with a knee implant was also scanned following IRB guidelines using: TE/TR=7.5/2900ms, matrix-size=320x256x40, FOV=18x18x16cm$$$^3,\:$$$parallel-imaging=2x2, and acquisition-time=6.7 minutes. All scans/simulations used or assumed a GE 3.0T MR750 scanner (GE Healthcare, Waukesha, WI) with spectral bin spacing of 1kHz and 22 bins ranging from -11kHz to 10kHz.

Figure 3 shows the results of the simulated phantom, including the field-map error using both estimation methods, and bin combined images. Here we see that matched filter field-map estimation is both less noisy and less biased than the current method.

The agar phantom and in vivo knee results are shown in Figures 4 and 5 respectively. These show, as do Figure 3, that the proposed method performs well at deblurring and leads to significantly less distortion near the metallic implant.

While the matched filter field-map estimate is generally not biased, it may be biased when the full bin profile is not visible due to the limited number of bins acquired. Additionally, there are regions where the off-resonance is rapidly varying, which results in a small field-map estimation bias for the matched filter method. This is likely because the signal is either compressed or stretched [2], depending on the slope of the off-resonance, within a bin, creating ambiguity in the field-map estimation. Additionally, while the proposed deblurring method performs well, in regions where the goodness-of-fit is low the algorithm errs on the side of less distortion at the expense of not fully correcting the blur.We have shown a method for improved field-map estimation and deblurring in MAVRIC-SL. This method creates images with less noise and significantly reduced distortion near the metallic implant when compared to current deblurring techniques.