MRI-guided PET image denoising using a non-local means filter
Marie Anne Richard1, Réjean Lebel1, Jérémie P. Fouquet1, and Martin Lepage1

1Centre d'imagerie moléculaire de Sherbrooke, Université de Shebrooke, Sherbrooke, QC, Canada

### Synopsis

Positron emission tomography (PET) images suffer from statistical noise, especially in short time frames. For applications requiring high temporal resolution, such as dynamic studies, efficient edge-preserving denoising algorithms such as the non-local means filter (NLMF) are needed. Because this filter relies on structural data, coregistered MR images were used to guide the NLMF. This novel method was compared to conventional PET-guided NLMF and proved superior in terms of increased contrast-to-background ratio and signal-to-noise ratio in a phantom model. It also increased small structure resolution in a rat model.

### Purpose

To leverage MRI for denoising positron emission tomography (PET) images using structural information.

### Context

Dynamic studies in PET are limited by noise due to the low number of events detected during short time frames. There is a need for powerful, fast denoising algorithms.

### Theory

Noise can be efficiently reduced by averaging the values of several similar voxels in an image. However, choosing the appropriate similarity criteria is essential. Simply assuming image smoothness and averaging neighboring voxels will result in loss of edge sharpness, making it difficult to pinpoint the boundaries of structures. The non-local mean filter (NLMF) averages voxels that are not necessarily close spatially, but are located in similar regions1. To do so, it assigns a filter weight, w, to each voxel, q, based on how similar the intensity of its neighborhood is compared to that of the voxel, p (Fig. 1). Therefore, the intensity I of p is given by the following weighted sum:$$I(p)=I(q_1)w(p,q_1)+I(q_2)w(p,q_2)+...$$ The effect is an edge-preserving filter that has been found useful in denoising PET and MRI images2,3.

### Hypothesis

Using an MR image to incorporate structural priors in the NLMF will improve small structure resolution and signal recovery in the PET image.

### Methods

A NEMA NU 4-2008 phantom (Data Spectrum Corporation) containing 11.2 MBq of fluorodeoxyglucose in 18 ml water and a glioblastoma-bearing rat injected with fluoroethyltyrosine were imaged on the LabPET4 small-animal PET scanner (Gamma Medica/GE Healthcare). Multiple time frame reconstruction was performed with a maximum likelihood expectation maximization algorithm using 20 iterations. MRI was also performed on a 7T small-animal scanner (Varian) to acquire images of the phantom (20 slices; resolution 0.156*0.156*2 mm) and the rat (DCE‑MRI; 10 slices; resolution 0.125*0.125*1 mm). The PET and MRI images were resampled to PET resolution and automatically coregistered in ANTs using a mutual information criterion. For the phantom, PET images were filtered using the NLMF in two conditions: 1) filter weights based on the PET data; 2) weights based on the MRI data. The filtering process took about 2 minutes in both cases. Afterwards, regions of interest (ROI) corresponding to each hot spot and to the background were manually drawn on the MR image and copied on the coregistered PET images. The contrast-to-background ratio and the mean-to-standard deviation of the ROI signal (proportional to the signal-to-noise ratio) were calculated for the filtered and unfiltered PET images. For the rat, only qualitative data are presented here.

### Results

On visual inspection, filtered images show sharper edges and improved resolution of small objects (Fig. 2 and 3). However, the signal of the 1 mm hot spot remains low. In all cases, MRI-based NLMF increases contrast-to-background ratio (Table 1-A) compared to the unfiltered image; whereas, the PET-based NLMF tends to decrease it. Moreover, the mean-to-standard deviation of the ROI signal generally increases in filtered images (Table 1-B). Again, the MRI-based NLMF is superior to the PET-based NLMF in all but one ROI. Finally, the intensity profiles (Fig 4) of the ROI are similar in terms ROI width, although filtered image show a more homogeneous repartition of the signal in the ROI. The areas under these profiles are the same.

### Discussion

Applying the NLMF to PET images decreases the noise level allowing smaller, less intense, structures to emerge both in phantom and in vivo data. However, resolution is still limited by partial volume effects. For example, the 1 mm ROI shows only 12 % of the actual activity because of spill-out. For this reason, it cannot be resolved even after denoising. Nevertheless, there is a gain in contrast-to-background and signal-to-noise ratio when using the MRI-based NLMF compared to the PET-based version. This was expected because the NLMF method relies on structural details present in the image and MRI provides better spatial resolution. Finally, the similar intensity profiles between the raw PET image and both filtered images confirm that this method does preserve edge sharpness and total signal.

### Conclusion

The MRI-based NLMF has proven fast and effective to denoise PET phantom and in vivo data. Because MRI and PET images are often acquired in pairs, this method could be widely used in the clinical and preclinical settings. It has also the potential to increase signal-to-noise ratio in short time frames making it useful for dynamic studies. However, to fully recover the PET tracer concentration, this denoising should be coupled to a partial volume correction algorithm, which could be MRI-guided.

### Acknowledgements

This work is funded by the NSERC and FRQNT.

### References

References [1] Buades et al. Multiscale Model Simul. 2005; 4(2):490-530. [2] Coupé et al. IEEE Trans. Med. Imag. 2008; 27(4):425:441. [3] Dutta et al. PLoS One. 2013;8(12):e81390.

### Figures

Figure 1. Non-local means filtering of a PET image. The value of the filtered voxel, p, is the weighted average of voxels, qn. The weights, w, are assigned based on the similarity between the regions bordering the voxels. Therefore, q1 contributes more to the value of p than q2.

Figure 2. Axial view of the phantom with 5 hot spots. The PET images show the first 30 seconds of a 5 minutes acquisition. The bottom images have been filtered, respectively with the PET-guided and MRI-guided non-local means filter.

Figure 3. Dynamic series of a glioblastoma-bearing rat brain imaged with fluoroethyltyrosine. Images are shown before and after the application of the MRI-guided non-local means filter.

Figure 4. A) Profile line drawn on the PET image. B) Intensity profile of the 2 mm ROI in the filtered and unfiltered PET images.

Table 1. Ratio of the average hot spot intensity A) to the average background intensity and B) to the standard deviation (proportional to the signal-to-noise ratio). The highest ratio for a region is indicated in red.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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