Dynamic PET denoising using Robust PCA

Abstract

Many denoising methods for dynamic positron emission tomography (PET) have been proposed such as conventional Gaussian spatio-temporal smoothing, Principle Component Analysis (PCA) based denoising, HighlY constrained backPRojection (HYPR), and Non-Local Means (NLM) based methods. We investigated robust PCA, that was originally proposed by Candes et al., as a potential alternative for dynamic PET denoising. Robust PCA decomposes a large data matrix M into the sum of a low rank matrix L and a sparse matrix S by an iterative optimization procedure. We conjecture that slowly varying activity over time corresponds to low rank components L and noise / sudden activity changes can be represented as sparse components S. We performed robust PCA for 4-D dynamic PET (3-D volume with time) and slice-by-slice dynamic PET (2-D multi-slice with time) with 18 F dynamic PET data (126 x 126 x 117 voxels with 54 frames) from an animal study with two rats. Our proposed methods yield promising decomposition results for dynamic PET denoising. Our robust PCA with 4-D PET data yielded more temporally smooth low rank volume sequences than slice-by-slice dynamic PET. Initial visual quality assessment confirmed our conjecture and indicated that robust PCA does not only separate noise in sparse matrix S, but also separate sudden activity changes such as initial injection of activity unlike other methods such as 4-D Gaussian or HYPR. Further quantitative analysis with Monte Carlo simulation will be required to fairly compare our proposed methods with previous dynamic PET denoising methods.