  Low-resolution and signal-dependent noise distribution in positron emission
tomography (PET) images makes denoising process an inevitable step prior to
qualitative and quantitative image analysis tasks. Conventional PET denoising
methods either over-smooth small-sized structures due to resolution limitation
or make incorrect assumptions about the noise characteristics. Therefore,
clinically important quantitative information may be corrupted. To address
these challenges, we introduced a novel approach to remove signal-dependent
noise in the PET images where the noise distribution was considered as
Poisson-Gaussian mixed. Meanwhile, the generalized Anscombe's transformation
(GAT) was used to stabilize varying nature of the PET noise. Other than noise
stabilization, it is also desirable for the noise removal filter to preserve
the boundaries of the structures while smoothing the noisy regions. Indeed, it
is important to avoid significant loss of quantitative information such as
standard uptake value (SUV)-based metrics as well as metabolic lesion volume.
To satisfy all these properties, we extended bilateral filtering method into
trilateral filtering through multiscaling and optimal Gaussianization process.
The proposed method was tested on more than 50 PET-CT images from various
patients having different cancers and achieved the superior performance
compared to the widely used denoising techniques in the literature.
