Date of Award


Degree Type


Embargo Date


Degree Name

Doctor of Philosophy (PhD)




Andrzej Krol

Second Advisor

Edward Lipson


Cone Beam, Mesh, Micro CT, SPECT, System Matrix, Tomographic Image Reconstruction

Subject Categories



The purpose of this study was to contribute to the advancement of statistically-based iterative reconstruction algorithms and protocols for both SPECT and micro CT data. Major contributions of this work to SPECT reconstruction include formulation and implementation of fully three-dimensional voxel-based system matrix in parallel-beam, fan-beam, and cone-beam collimator geometries while modeling the process of attenuation, system resolution and sensitivity. This is achieved by casting rays through a volume of voxels and using ray-voxel intersection lengths to determine approximate volume contributions. Qualitative and quantitative analysis of reconstructed Monte Carlo data sets show that this is a very effective and efficient method. Using this method, three SPECT studies were conducted.

First, the reconstruction performance was studied for a triple-head cone-beam SPECT system using a helical orbit acquisition. We looked at various subset groupings for the ordered-subsets expectation maximization (OSEM) algorithm. We also examined how rotational and translational sampling affects reconstructed image quality when constrained by total injected dose and scan time. We conclude the following: When reconstructing noiseless datasets, varying the rotational sampling from 90 views to 360 views over 360 degrees does not affect the reconstructed activity regardless of the object size in terms of both convergence and accuracy. When using ordered subsets, the subset group arrangement is important in terms of both image quality and accuracy. The smaller the object is that is being reconstructed, the rate of convergence decreases, the spatial resolution decreases, and accuracy decreases.

Second, we examined a system composed of three, possibly different, converging collimators using a circular orbit. We conclude the following: When reconstructing noiseless datasets, using a triple-cone beam system resulted in distortion artifacts along the axial direction and diminished resolution along the transaxial direction. Using a triple-fan beam system resulted in the best reconstructed image quality in terms of bias, noise, and contrast. When noisy datasets were reconstructed, a cone-cone-fan beam system resulted in best reconstructed image quality in terms of mean-to-actual ratio for small lesions and a triple-fan beam system for large lesions.

Finally, a two-dimensional mesh-based system matrix for parallel-beam collimation with attenuation and resolution modeling was designed, implemented, and studied. We conclude that no more than two divisions per detector bin width are needed for satisfactory reconstruction.

Also, using more than two divisions per detector bin does not significantly improve reconstructed images. A chapter on iterative micro-CT reconstruction is also included. Our contribution to micro-CT reconstruction is the formulation and implementation of a cone-beam system matrix that reduces ring artifacts associated with sampling of the reconstruction space. This new approach reduces the common 3 D ray-tracing technique into 2-D, making it very efficient. The images obtained using our approach are compared to images reconstructed by means of analytical techniques. We observe significant improvement in image quality for the images reconstructed using our iterative method.


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