A noise smoothing origin ensemble algorithm based on local filtering

Abstract

An origin ensemble (OE) image reconstruction algorithm can be used for the fast reconstruction of unconventional geometrical images, e.g. in a Compton camera (CC) system. Due to the low-count rate in the emission data, the reconstructed image is often noisy and inhomogeneous in density. In this study, we propose a way to smooth out the noise in the OE algorithm. During the OE reconstruction, the algorithm stochastically modifies the current location to a random new voxel along the probable corresponding curve of each event depending on the relative event density of the new and old locations. In the original OE technique, the event density is simply the number of events in the voxel. In the proposed method, the event density is estimated from the filtering of a kernel window centered on the voxel. Incorporating the regional filtering is similar to performing an OE algorithm on a smoothed image at each iteration and enables the reconstruction of a smoother image. A Flangeless Esser PET phantom and a multi-activity phantom are used to study the property of the new reconstruction algorithm. The results indicate that the proposed method performs better than a conventional OE algorithm in terms of normalized mean square error (NMSE) and structural similarity (SSIM). Both contrast noise ratio (CNR) and reconstruction accuracy of the new method are better than the conventional OE algorithm and their performances improve with the increase of object size. The median-OE possesses the highest overall image quality and recovery rate among the three filter-OE algorithms and is the method of choice for image reconstruction. Comparing to conventional post-smoothing OEs, the NMSE of median-OE improves 57.6% (46.9%) and the SSIM increased by 73.2% (51.1%) for the Esser (multi-activity) phantom. The proposed OE algorithm is simple and efficient for noise smoothing without complex calculations and highly suited for low-count cases.