Abstract
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Objectives: Image denoising is useful and important in PET imaging. The most popular denoising approach in commercial PET scanners is still Gaussian post-filtering due to its linearity and robustness, even though the images are blurred during noise reduction. There have been many efforts to improve PET denoising, aimed at noise reduction while preserving image texture and contrast. Several non-linear filters such as AD, NLM, DCNN etc. have been investigated for PET denoising but unfortunately all of them require complicated parameter tuning which puts them at a disadvantage compared to simple Gaussian post-filtering. Furthermore, a single set of parameters can’t be used for all images as different images have different scale values and noise levels. In most cases, if the parameters are not tuned well, not only will the filter performance be suboptimal but there will also likely be unnatural image textures and artifacts in the smoothed images. This presents a huge barrier for the clinical implementation of non-linear filters despite the many publications that have demonstrated superior performance over Gaussian filters. In this work, we propose a parameter tuning algorithm for non-linear filters, so that they can be adaptively used under multiple clinical PET imaging conditions without user intervention. We implemented the parameter tuning algorithm for the Non-local Means (NLM) filter.
Methods: For a given discrete noisy image , the smoothed result at voxel from the NLM filter is computed according to a weighted average of neighbor voxels, and the weight w(i,j) is based on the similarity between voxels i and j. Image intensity values in the respective local neighborhoods (called patches) of voxels i and j are used to calculate w(i,j). These patches are denoted by Niand Nj, respectively. The difference between the patches is used to define the similarity between the two pixels with an isotropic Gaussian kernel as: w(i,j)=exp{-||f(Ni)-f(Nj)||2/h2}, where || ||2 denotes the Euclidean distance. The parameter h controls the smoothness strength and is a user-selected value. The contribution of a voxel to another voxel’s filtered value is determined by the ratio of ||f(Ni)-f(Nj)||2 and h2. We propose an adaptive strength for NLM where the weights are calculated according to h=u(i)*k. u(i) is the weight map that allows the weight to accommodate different cases and is a constant. In order to obtain the u(i) map, a local standard deviation (STD) is calculated for each voxel. In order to avoid lesions producing higher STD in a local neighborhood, a median filter is applied to the STD map. From the definition of , we can see that gets automatically adjusted to different image scales because STD is proportional to the image mean. Therefore, the input image does not need to be normalized prior to smoothing. Furthermore, STD is also proportional to the noise level, therefore will also be automatically adjusted to different noise levels.
Results: In our experiments, we applied this filtering approach to both phantom and patient datasets from Canon’s digital TOF-PET/CT scanner with IRB approval and patient’s consent for patient datasets. PET data was reconstructed with fully 3D list-mode TOF ordered-subset expectation-maximization (OSEM) with full physical corrections, including image-based point spread function (PSF) modeling. We can see that the proposed parameter selection can make the NLM filter adaptive to images reconstructed from a wide range of data noise levels, reconstructed with different reconstruction settings. In all cases, the filtered images outperformed Gaussian post-smoothed images, resulting in both smoother backgrounds and also higher lesion contrasts.
Conclusions: In this work, we proposed an automatic parameter tuning method for non-linear post-filters. With this method, the NLM algorithm can be used in different PET data acquisition and image reconstruction settings, producing quantitatively and qualitatively high-quality images without any parameter adjustments by the user.
