Fully 4D dynamic image reconstruction by nonlinear constrained programming

Abstract

Abstract-In standard SPECT with static radio-tracers, the activity distribution in tissue is assumed constant during the acquisition. However, techniques capable of visualizing dynamic tracers may provide new insight into physiology and function of organisms. This is the aim of dynamic SPECT. We developed oSPECT, a new fully 4D reconstruction approach to obtain time activity curves from single or multiple slow rotations with dynamic SPECT data. It is based on KNITRO, a large-scale nonlinear constrained optimization method that takes curvature information into account to speed up convergence. The performance of oSPECT is tested using data from a dynamic anthropomorphic numerical phantom that simulates myocardial perfusion of 99mTc-Teboroxime. We also tested the method on a simulated brain study with 123I-FP-CIT, a dynamic presynaptic marker for SPECT of the dopaminergic neurotransmission system.

Electron tomography: a short overview with an emphasis on the absorption potential model for the forward problem

“…Remark 4.2. Since u in fulfils (6) and since (7) and ( 9) holds, the wave equation for the scattered part u sc is given as…”

“…The filtered back-projection method is still the most widely used reconstruction method in ET. In order to apply the FBP method, one needs to assume that data are modelled as in (30) and the forward operator yields the actual measured data 6 . With appropriate post-processing, as explained in [136], one can then recast the inverse problem in ET (given by definition 7.3) as the problem of inverting the x-ray transform given its (noisy) samples on a parallel beam line complex.…”

“…Blind deconvolution is an example of a multi-component inverse problems where one seeks to deconvolve when the convolution kernel is unknown. Another example is the identification problem in emission tomography where both the attenuation map and the activity map are unknown and needs to be reconstructed from measured data[6,74].…”