Fast Regularization Design for Tomographic Image Reconstruction for Uniform and Spatial Resolution.

Tomographic Reconstruction;Regularization;Iterative Reconstruction;Spatial Resolution;Engineering;Electrical Engineering: Systems

Shi, Hugo R.Sadanandarao, Sandeep P. ;

University of Michigan

关键词: Tomographic Reconstruction;    Regularization;    Iterative Reconstruction;    Spatial Resolution;    Engineering;    Electrical Engineering: Systems;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/61554/hugoshi_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Statistical methods for tomographic image reconstruction have improved noise and spatialresolution properties that may improve image quality in X-ray CT and PET. Finalconverged solutions from maximum likelihood (ML) and weighted least squares (WLS)reconstruction are often extremely noisy due to the ill conditioned nature of the system.One can stop the iterative algorithm before convergence and before images become toonoisy, however this results in non-uniform and anisotropic spatial resolution because resolutionuniformity and isotropy improve with successive iterations. Alternatively, one canrun the iterative algorithm to completion and post-filter the resulting noise, however, thisoften requires a large number of iterations. Instead we use penalized likelihood (PL) andpenalized weighted least squares (PWLS) with a roughness penalty to regularize the problemwhich filters out noise, and leads to faster convergence. Unfortunately, interactionsbetween the weightings, which are implicit in PL methods and explicit in PWLS methods,and conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution.Previous work focuses on matrix algebra methods to design data-dependent, shiftvariant regularizers that improve resolution uniformity. This thesis develops fast analyticalregularization design methods for 2D fan-beam X-ray CT imaging, for which parallelbeamtomography is a special case. This thesis uses continuous space analogs to greatlysimplify the regularization design problem which yields a mostly analytical solution forefficient computation. This thesis extends regularization design to 3D systems using acomputationally efficient iterative approach. Finally, this thesis explores using 2D regularizationwith z-dimension post-reconstruction denoising. This is an attempt to combinethe improved XY isotropy associated with 2D regularization design, and the computationalefficiency of the mostly analytical solution and use it for 3D geometries. The spatialresolution and noise properties of this method is analyzed for quadratic regularizers. Simulationresults have also been performed using non-quadratic edge-preserving regularizerswhich show that, though this method has potential, more work needs to be done to ensurethat the spatial resolution and noise properties of this method are desirable.