Spatio-temporal Reconstruction of dPET Data Using Complex Wavelet Regularisation

Traditionally, dynamic PET studies reconstruct temporally contiguous PET images using algorithms which ignore the inherent consistency between frames. We present a method which imposes a regularisation constraint based on wavelet denoising. This is achieved efficiently using the Dual Tree - Complex Wavelet Transform (DT-CWT) of Kingsbury, which has many important advantages over the traditional discrete wavelet transform: shift invariance, implicit measure of local phase, and directional selectivity. In this paper, we apply the decomposition to the full spatio-temporal volume and use it for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using traditional wavelet thresholding schemes we introduce a locally defined and empirically-determined Cross Scale regularisation technique. We show that wavelet based regularisation has the potential to produce superior reconstructions and examine the effect various levels of boundary enhancement have on the overall images. We demonstrate that wavelet-based spatio-temporally regularised reconstructions have superior performance over conventional Gaussian smoothing in simulated and clinical experiments. We find that our method outperforms conventional methods in terms of signal-to-noise ratio (SNR) and Mean Square Error (MSE), and removes the need to post-smooth the reconstruction.