三维圆柱形PET二次正则化设计

H. Shi, J. Fessier
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引用次数: 7

摘要

层析成像的统计重建方法提高了PET的空间分辨率和噪声特性。惩罚似然(PL)图像重建方法涉及最大化目标函数,该目标函数基于正弦图测量的对数似然和粗糙度惩罚函数来控制噪声。在发射层析成像中,基于常规二次正则化函数的PL方法(和MAP方法)导致非均匀和各向异性的空间分辨率,即使对于理想的平移不变成像系统也是如此。我们之前已经解决了平行波束二维发射层析成像和扇形波束二维透射层析成像的这个问题,通过设计数据相关的位移变量正则器来提高分辨率均匀性和各向同性,甚至对于理想的位移不变成像系统也是如此。本文将这些方法扩展到三维圆柱形PET,使用一种数值有效的分析设计方法。
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Quadratic regularization design for 3D cylindrical PET
Statistical methods for tomographic image reconstruction lead to improved spatial resolution and noise properties in PET. Penalized-likelihood (PL) image reconstruction methods involve maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In emission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam 2D emission tomography, and for fan-beam 2D transmission tomography by designing data-dependent, shift-variant regularizers that improve resolution uniformity and isotropy, even for idealized shift-invariant imaging systems. This paper extends those methods to 3D cylindrical PET, using an analytical design approach that is numerically efficient.
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