Application of SAGE algorithm in PET image reconstruction using modified ordered subsets

A new method that uses a modified ordered subsets （MOS） algorithm to improve the convergence rate of space-alternating generalized expectation-maximization （SAGE） algorithm for positron emission tomography （PET） image reconstruction is proposed.In the MOS-SAGE algorithm,the number of projections and the access order of the subsets are modified in order to improve the quality of the reconstructed images and accelerate the convergence speed.The number of projections in a subset increases as follows：2,4,8,16,32 and 64.This sequence means that the high frequency component is recovered first and the low frequency component is recovered in the succeeding iteration steps.In addition,the neighboring subsets are separated as much as possible so that the correlation of projections can be decreased and the convergences can be speeded up.The application of the proposed method to simulated and real images shows that the MOS-SAGE algorithm has better performance than the SAGE algorithm and the OSEM algorithm in convergence and image quality.

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.