Non-local means denoising of dynamic PET images

Abstract

Objective: Dynamic positron emission tomography (PET), which reveals information about both the spatial distribution and temporal kinetics of a radiotracer, enables quantitative interpretation of PET data. Model-based interpretation of dynamic PET images by means of parametric fitting, however, is often a challenging task due to high levels of noise, thus necessitating a denoising step. The objective of this paper is to develop and characterize a denoising framework for dynamic PET based on non-local means (NLM).

Theory: NLM denoising computes weighted averages of voxel intensities assigning larger weights to voxels that are similar to a given voxel in terms of their local neighborhoods or patches. We introduce three key modifications to tailor the original NLM framework to dynamic PET. Firstly, we derive similarities from less noisy later time points in a typical PET acquisition to denoise the entire time series. Secondly, we use spatiotemporal patches for robust similarity computation. Finally, we use a spatially varying smoothing parameter based on a local variance approximation over each spatiotemporal patch.

Methods: To assess the performance of our denoising technique, we performed a realistic simulation on a dynamic digital phantom based on the Digimouse atlas. For experimental validation, we denoised [Formula: see text] PET images from a mouse study and a hepatocellular carcinoma patient study. We compared the performance of NLM denoising with four other denoising approaches - Gaussian filtering, PCA, HYPR, and conventional NLM based on spatial patches.

Results: The simulation study revealed significant improvement in bias-variance performance achieved using our NLM technique relative to all the other methods. The experimental data analysis revealed that our technique leads to clear improvement in contrast-to-noise ratio in Patlak parametric images generated from denoised preclinical and clinical dynamic images, indicating its ability to preserve image contrast and high intensity details while lowering the background noise variance.

Figure 1. Similarity computation.

The similarity between a voxel and a voxel , given by (3), is derived from spatiotemporal patches at the two voxels, composed of the local spatial neighborhood (denoted for voxel ) and all time points beyond a temporal threshold . The pairwise weights can be assembled into a symmetric matrix of similarities as shown.

Figure 2. Dynamic digital mouse phantom.

(a) Coronal slices of the Digimouse atlas showing the spatial distribution of distinct tissue types used in simulation. (b) Decay-corrected and averaged TACs corresponding to each manually delineated tissue type extracted from a dynamic PET image of a mouse. The color codes for different tissue types used for both the spatial map and the TACs are indicated in the legend.

Figure 3. Plots of bias vs. standard deviation.

Percentage bias vs. percentage standard deviation plots are shown for the 11 ROIs (indicated in figure 2) and for the overall phantom volume for the noisy and denoised dynamic images. Of the five denoising methods compared (Gaussian, PCA, HYPR, NLM-S, and NLM-ST), NLM-ST simultaneously yields lowest bias and lowest standard deviation for a majority of the individual ROIs and also for the overall volume.

Figure 4. A coronal slice from the dynamic Digimouse phantom.

The rows represent the true, noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images respectively. The columns represent three time points (289 s, 619 s, and 2264 s) reflecting the evolution of activity over time. The columns correspond to time bin sizes of 120 s, 160 s, and 550 s from left to right. Accordingly, the left and middle columns are noisier than the right column.

Figure 5. Patlak parametric imaging for the digital phantom study.

(a) The Patlak influx constant was computed from the true, noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images of the dynamic Digimouse phantom. (b) Plots of overall percentage bias vs. percentage standard deviation for the Patlak parametric images computed from the noisy and denoised dynamic images.

Figure 6. A coronal slice from the dynamic PET image of a mouse.

The rows represent the noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images respectively. The columns represent three time points (169 s, 619 s, and 2264 s from left to right) reflecting the evolution of activity over time. The white arrows pinpoint extra uptake in the skin in the later frames of the PCA-denoised image, which appears to be an image artifact.

Figure 7. Patlak parametric imaging for the preclinical study.

(a) The Patlak influx constant was computed using noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images from an PET mouse study. (b) The top row delineates the signal (red) and background (blue) ROIs used for evaluation. The middle row shows the percentage recovered signal in the hot regions for different denoising methods. The bottom row shows the CNR in the Patlak parametric images, measured as the ratio of the contrast between the signal and the background ROIs to the standard deviation in the background.

Figure 8. A transverse slice from the dynamic PET image of a patient with hepatocellular carcinoma.

The rows represent the noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images respectively. The columns represent three time points (67.5 s, 390 s, and 3300 s from left to right) reflecting the evolution of activity over time.

Figure 9. Patlak parametric imaging for the clinical study.

(a) The Patlak influx constant was computed using noisy, Gaussian-denoised, PCA-denoised, HYPR-denoised, NLM-S denoised, and NLM-ST denoised images from an PET scan of a patient with hepatocellular carcinoma. (b) The top row delineates the signal (lesions marked in red) and background (spleen marked in blue) ROIs used for evaluation. The middle row shows the percentage recovered signal in the hot lesions for different denoising methods. The bottom row shows the CNR in the Patlak parametric images, measured as the ratio of the contrast between the signal and the background ROIs to the standard deviation in the background.