Abstract
Imaging systems are often modeled as continuous-to-discrete mappings that map the object (i.e. a function of continuous variables such as space, time, energy, wavelength, etc) to a finite set of measurements. When it comes to reconstruction, some discretized version of the object is almost always assumed, leading to a discrete-to-discrete representation of the imaging system. In this paper, we discuss a method for single-photon emission computed tomography (SPECT) imaging that avoids discrete representations of the object or the imaging system, thus allowing reconstruction on an arbitrarily fine set of points.
Highlights
Mathematical tomography centers around integral transforms in which both the object and the image are treated as functions of continuous variables; we refer to an integral transform as a continuous-to-continuous (CC) operator.The ubiquitous practice of representing real-life objects with a finite set of intensities over a 2D or 3D grid of pixels or voxels often leads to inaccuracies when the object itself presents many features that cannot be represented using a grid of pixels or voxels
We discuss our approach to approximating CC operators for real single-photon emission computed tomography (SPECT) imaging systems in which we use measured calibration data from real detectors and real multi-pinhole imaging systems, potentially avoiding discrete representations of the object or the raw data
We presented a new approach to image reconstruction for single-photon emission computed tomography (SPECT) that does not use a discrete-to-discrete representation of the imaging system
Summary
Mathematical tomography centers around integral transforms in which both the object and the image are treated as functions of continuous variables; we refer to an integral transform as a continuous-to-continuous (CC) operator. Similar to Barrett et al (1997) and Parra and Barrett (1998), our algorithm assumes that the list-mode data are positions of interaction as estimated (Moore et al 2007) from data collected with the gamma-ray cameras in the SPECT scanner. These estimates are allowed to vary over a continuous domain, and probability density functions are evaluated on-the-fly for each item of the list. This paper is an extended version of the conference proceeding (Caucci et al 2015a) presented by the authors at the 13th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (‘Fully 3D 2015’) held in Newport, Rhode Island, USA
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