3D discrete ridgelet transform for emission tomography denoising

Denoising in emission tomography is a quite challenging task due to the inherent low signal-to-noise ratio of the acquired data. In clinical routine there is often no post reconstruction denoising step on the acquired images. Spatial filtering (e.g. via Gaussian smoothing) may be used to reduce the noise but it leads to blurring of the image and while it increases the Signal to Noise Ratio (SNR), it also leads to a loss of resolution. Our objective was therefore to propose a new methodology to process emission tomography images in order to improve SNR with no or few impact on the spatial resolution. Different improved denoising techniques have been introduced and many are based on the wavelet transform. This latter however present some limitations due to its non optimal processing of edges discontinuities, because discontinuities across a simple edge affect all the wavelets coefficients on the edge. In this study, we studied the use of a new transform for emission tomography denoising, namely the ridgelet transform and more precisely its 3D discrete implementation called 3D DART. This latter extends the wavelet approach in order to take into account the edge discontinuities. We performed a comparison study between the wavelet and the ridgelet transform considering the same parameters and for different synthetic, simulated and clinical emission tomography images. The ridgelet and wavelet methodologies lead to similar quantitative denoising regarding the SNR. However, due to its edge preserving ability, the ridgelet transform leads to lower resolution loss than the wavelet approach. Such a technique is therefore a promising tool for emission tomography denoising.