Wavelet-based pre-smoothing and post-denoising for iterative image reconstruction for emission tomography

A wavelet-based smoothing technique based on hard and soft thresholding is proposed to eliminate statistical noise interference in the reconstruction of emission computed tomography. The interference is due to Poisson noise in the projection data. Pre-smoothing for projection data is performed to reduce the noise interference, together with post-smoothing for reconstructed images from the pre-smoothed projection data. The present work also investigates not only optimal parameter values for hard and soft thresholding but also the reason why the parameter values produced good smoothing results. An analysis was made about parameter values for thresholding with which good smoothing results were produced for the purpose of explaining the reason. Based on this analysis, an ad-hoc denoising algorithm is proposed for pre- and post- smoothing.