Supervised diffusion parameter selection for filtering SPECT brain images

Abstract

Iterative image reconstruction from noisy data requires regularization to avoid noise amplification in the reconstructed image at high iteration numbers. This is often accomplished by stopping the iteration process at a relatively low number of iterations or by post filtering the reconstructed image. The aim of this paper is to investigate whether stopping is better than post-filtering, and to determine suitable filter functions for Single Photon Emission Computed Tomography (SPECT). As a study example for finding filter functions for a particular imaging situation, projections of a Tc-99m emitting brain phantom are generated by a SPECT simulator which includes effects of the distance dependent camera response, attenuation, scatter and Poisson noise. Iterative reconstructions are performed using three different camera response models, resp. (i) only attenuation (A), (ii) attenuation and camera response (AD) and (iii) attenuation, camera response and scatter (ADS). Optimal filter parameters for each reconstruction are estimated by parameter selection procedures which minimize image differences between the phantom and the filtered SPECT images. 3D linear diffusion (Gaussian filtering) and 3D nonlinear diffusion (Catté scheme) are used. For the Gaussian filter, the parameters to be optimized are the kernel widths in the transaxial plane and the axial direction. Furthermore, the Gaussian filter function allows the widths to change as a function of the distance to the transaxial axis. The Catté scheme is parameterized by the local smoothing as a function of the image gradient, the spatial resolution at which the gradient is calculated, and the “time-step”. It has been shown for the Gaussian filter that in the case of ADS the difference between the phantom and the filtered reconstruction in terms of the normalized mean squared error (NMSE) is significantly reduced by optimal (i.e, minimum NMSE) filtering compared to early stopping the iterative reconstruction, and the low NMSE is quite stable at high iteration numbers. In the cases of A, AD and ADS: (i) only a small additional reduction of the NMSE is accomplished by including also invariance and anisotropy of the filter kernel; (ii) at high iteration numbers, the transaxial width of the kernel gets closer to the axial width; (iii) although some image features are better preserved by Catté, the NMSE is not further reduced compared to Gauss. This is consistent with our findings that the optimum Catté scheme converges to Gaussian blurring. Using accurate image formation models during iterative reconstruction is more important than the choice of the filter function.