Noise properties of regularized image reconstruction in X -ray computed tomography.

Abstract

X-ray computed tomography (CT) has routine use in medical diagnosis. Technology advancements enable further clinical applications, such as cardiac imaging and lung cancer screening. It also has use in industrial applications. The spatial resolution and noise properties of image reconstruction methods are important for imaging system design, reconstruction method comparisons and reconstruction parameter selection. Current reconstruction methods fall into two main categories: analytical and iterative methods. The representative of the former category is filtered back projection (FBP) or convolution back projection (CBP). The iterative methods can be further divided into algebraic and statistical methods. The spatial resolution and noise properties of analytical methods are well studied and understood. The statistical reconstruction methods have the potential to offer improved image quality and better bias-variance performance. They are based on models for measurement statistics and physics, and can easily incorporate the prior information, the system geometry and the detector response. They can also model Compton scattering and the polyenergetic spectrum of the X-ray source. The main disadvantages of the statistical reconstruction methods are the longer computation time of iterative algorithms that is usually required to minimize certain cost functions, and the lack of insights into the resolution and noise properties of the reconstructed images. This thesis addresses these two concerns of statistical reconstruction methods by developing the fast non-uniform FFT (NUFFT)-based forward and back-projectors and by deriving an analytical approach to study the noise properties of the statistically reconstructed images. The overall computation for the NUFFT based 2D fan-beam forward projector is akin to previous hierarchical methods, and is about two times faster than the distance-driven (DD) forward projector while providing comparable accuracy. The proposed analytical noise variance predictions for the 2D fan-beam geometry provide accuracy comparable to FFT-based predictions and agree well with empirical variances in fan-beam CT, but require much less computation than the traditional FFT method. An extension to 3D cylindrical CT is also developed.