Iterative algorithms for crystal efficiencies estimations from TOF compressed normalization data

The TOF clinical data are very sparse and have significant size. These data undergo TOF axial rebinning and azimuthal mashing if histogrammed data-based reconstruction algorithms are used. In a clinical environment, TOF compression is performed by the hardware rebinner. Normalization data, acquired on a regular basis and used for estimation of some norm components, are compressed by the hardware rebinner in a similar manner. In this paper we present simple update iterative algorithms for crystal efficiencies norm component estimation from TOF compressed normalization data. The previously known methods are not directly applicable, since the compression procedure significantly complicates normalization data model equations. Presented iterative methods have the advantages of easy adaptation to any acquisition geometry, and of allowing the estimation of parameters at the crystal level when the number of crystals is relatively small. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is investigated. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also derived. Measured normalization data from a Siemens prototype TOF scanner are used to validate the algorithms performance.