基于广义Gibbs先验的优质PET成像

Generalized Gibbs Priors in Positron Emission Tomography

最大后验方法(Maximum A Posteriori,MAP)已经广泛应用于解决图像重建中的病态问题,正电子发射成像(Positron Emission Tomography,PET)便是其中之一.本文基于MAP方法,针对PET成像提出一新的基于图像相似结构信息的广义Gibbs先验形式,新先验能在有效地抑制噪声的同时,鲁棒地保持锐利的边缘信息.但由于新先验的引入,使得重建模型的求解趋于复杂.为解决模型解的收敛性问题,我们提出两步式的局部线化优化迭代重建策略,并结合抛物线替代坐标上升(Paraboloidal Surrogate Coordinate Ascent,PSCA)算法进行求解.新算法分别对PET模拟数据和真实数据进行重建实验,结果表明本文提出的基于广义Gibbs先验的PET成像可以获得优质的重建图像.

Maximum A Posteriori （MAP） methods have been widely applied to the ill-posed problem of image reconstruc-tion,such as Positron Emission Tomography （PET） imaging. In this paper,a family of new generalized Gibbs priors based on MAP method, which exploits the basic affinity structure information in an image, is proposed. The generalized Gibbs priors can suppress noise effectively while capturing sharp edges without oscillations. A binary optimal reconstruction strategy is established using a lo-cally linearized scheme in the framework of a standard Paraboloidal Surrogate Coordinate Ascent （PSCA） algorithm. The proposed generalized Gibbs priors based MAP reconstruction algorithm has been tested on simulated and real phantom PET data. Comparisons of the new priors model with other classical methods clearly demonstrate that the proposed generalized Gibbs priors perform better in lowering the noise,and preserving the edge and detail in the image.