Date of Award

May 2016

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Edward Lipson

Second Advisor

Andrzej Krol


emisison computed tomography, iterative reconstruction, maximum a posteriori, penalized likelihood reconstruction, regularization, SPECT

Subject Categories

Physical Sciences and Mathematics


In PET and SPECT imaging, iterative reconstruction is now widely used due to its capability of incorporating into the reconstruction process a physics model and Bayesian statistics involved in photon detection. Iterative reconstruction methods rely on regularization terms to suppress image noise and render radiotracer distribution with good image quality. The choice of regularization method substantially affects the appearances of reconstructed images, and is thus a critical aspect of the reconstruction process. Major contributions of this work include implementation and evaluation of various new regularization methods. Previously, our group developed a preconditioned alternating projection algorithm (PAPA) to optimize the emission computed tomography (ECT) objective function with the non-differentiable total variation (TV) regularizer. The algorithm was modified to optimize the proposed reconstruction objective functions.

First, two novel TV-based regularizers—high-order total variation (HOTV) and infimal convolution total variation (ICTV)—were proposed as alternative choices to the customary TV regularizer in SPECT reconstruction, to reduce “staircase” artifacts produced by TV. We have evaluated both proposed reconstruction methods (HOTV-PAPA and ICTV-PAPA), and compared them with the TV regularized reconstruction (TV-PAPA) and the clinical standard, Gaussian post-filtered, expectation-maximization reconstruction method (GPF-EM) using both Monte Carlo-simulated data and anonymized clinical data. Model-observer studies using Monte Carlo-simulated data indicate that ICTV-PAPA is able to reconstruct images with similar or better lesion detectability, compared with clinical standard GPF-EM methods, but at lower detected count levels. This implies that switching from GPF-EM to ICTV-PAPA can reduce patient dose while maintaining image quality for diagnostic use.

Second, the 1 norm of discrete cosine transform (DCT)-induced framelet regularization was studied. We decomposed the image into high and low spatial-frequency components, and then preferentially penalized the high spatial-frequency components. The DCT-induced framelet transform of the natural radiotracer distribution image is sparse. By using this property, we were able to effectively suppress image noise without overly compromising spatial resolution or image contrast.

Finally, the fractional norm of the first-order spatial gradient was introduced as a regularizer. We implemented 2/3 and 1/2 norms to suppress image spatial variability. Due to the strong penalty of small differences between neighboring pixels, fractional-norm regularizers suffer from similar cartoon-like artifacts as with the TV regularizer. However, when penalty weights are properly selected, fractional-norm regularizers outperform TV in terms of noise suppression and contrast recovery.


Open Access