| Positron emission tomography (PET) is a noninvasive imaging technique that can provide information of biological and physiological process in vivo by measuring the spatial distribution of radioactive tracer.PET image reconstruction is a tradeoff issue between image resolution and calculation speed. Hence, developing optimizing algorithm to achieve acceptable processing time without sacrificing image quality is the key issue in this field. Based on state space theory, this paper will focus on further exploration covering the above two aspects:Firstly, in order to improve the spatial resolution and regularization of ill-conditioning problem, we expand our investigation into structural constraint. With the advantages of robust nature of Hoo filter and easy implementation of state space approach, an improved algorithm for PET image reconstruction is proposed by using segmented anatomical template that provided by other high quality imaging technology such as CT or MRI. Compared with other algorithms, experiments conducted by Monte carlo simulations indicate a persuasive assessment that the proposed strategy suppresses noise well, while the edges, boundary information and other details remain clear.Secondly, state space approach unifies PET reconstruction problem with state equation and observation equation respectively. And make it possible to fall into various strategies by adjusting these two expressions in terms of practical situation. However, the computational cost in matrix inversion is hindering this direct implementation of high dimensional data. In this paper, we adopt the methodology of LBFGS in linear optimization to yield the inversion part economically. And we mainly focus on static imaging and use Kalman filter(KF) to solve the two expression, as we confidently believe that the methodology in matrix reversion works similarly even situation changes. Experiment result verifies the improvement in computation efficiency with comparable image quality. |
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