Deterministic Modeling for Radiation Attenuation-integrated Radon Transform in Emission Computed Tomography: Algorithm, Curve Fitting Analysis, and Introduction of Attenuation Hadamard Matrix

Purpose: The purpose of the study is to propose an algorithm to implement and visualize radiation attenuation-integrated Radon transform based on Beer-Lambert law during emission computed tomography simulation using a deterministic model and also to perform image analysis on resulting images. Methods: Two types of phantoms are designed: plain-disk phantom and patterned-disk phantom. The large disk is filled with an activity of 5 units and the smaller disks have 10 units of activity of Tc-99m isotope as an emission map. Three transmission maps for patterned-disk phantom are created with uniform linear attenuation coefficient. Phantoms are scanned with 360 degrees and 180 degrees acquisition arcs. Then, using the algorithm designed, the exponential Radon transform is implemented. After that, the projections are back-projected and filtered to generate tomographic slices. Finally, all slices are analyzed using profile plotting and curve fitting. Moreover, an attenuation Hadamard matrix is provided to facilitate attenuation modeling. Results: The uniform intensity of activity in the phantoms is converted to a disk with progressively decreasing intensity from the periphery to the center in the tomographic slices. Similarly, the circles positioned more centrally appear less intense than those positioned in the periphery, despite all circles having equal activity. When the phantom is scanned in 180 degrees arc, the circles closest to the camera are visualized more intensely. The profile curves of the slices generated by exponential Radon transformation are depicted as U-shaped in profile plotting and are fitted to a bi-exponential function with a near-perfect precision. Conclusions: The incorporation of radiation attenuation results in the development of more realistic models for quantification purposes.