MODEL DETECTOR RESPONSE FUNCTION WITH A SKEW NORMAL DISTRIBUTION FUNCTION IN POSITRON EMISSION TOMOGRAPHY
Publication Date: 2015-Feb-24
The IP.com Prior Art Database
The present invention proposes a technique to improve PSF model estimation. The invention combines skew normal distribution technique and a technique to generate PSF kernels for PET scanner to improve characterization of a PET scanner and image reconstruction. Detector response function is modeled with a skew normal distribution by minimizing the sum of squared difference between data and estimated function.
The present invention relates generally to positron emission tomography (PET) and more particularly to a technique to model detector response function.
In PET imaging, system resolution is degraded by several factors, such as, size of detector crystal size and uncertainty about location of scintillation in the detectors. In order to recover
system resolution, a point-spread-function (PSF) is generally applied in image reconstruction to model detector response function. A commonly used PSF is in a form of normal distribution whose standard deviation describes magnitude of resolution degradation.
As the detector pair moves away from center of field of view (FOV), the detector response function attains asymmetry due to circular nature of scanner gantry. In a conventional technique the asymmetry is modeled by joining two half normal distributions. The two half normal distributions include two different standard deviations that describe detector response on left and right side of line-of-response (LOR) connecting a detector pair.
However, there are several limitations to the two-half normal distribution algorithm. For example, in order to estimate standard deviations of the left and the right half normal distribution, the acquired data requires division into two halves. One half is required for estimating parameters in left normal distribution and the other half is required for estimating parameters in right normal distribution. Asymmetry in the data generates unequal number of data points in the left half and the right half of the data. Consequently, unequal noise is generated in the estimated parameters for the two halves. For the most asymmetrical case, narrower half may have very few data points for a reliable estimation of standard deviation of the normal distribution. Further, division of data into two halves requires estimation of maximum data point. This is due to a possibility that actual maximum is not one of the data points. Figure 1 depicts data profile of a point source scan as a function of radial location and illustrates that actual maximum may not be one of the data points.
In the example given in Figure 1 above, intensity profile of a point source scan which is used to estimate the PSF is plotted as a function of radial distance from center of the FOV. Due to close values of the three highest data points it is difficult to determine the actual maximum. In order to divide the data into two halves, the actual maximum requires to be first estimated. As a result, uncertainty is created in the parameter estimation. Also, the example given in Figure 1 depicts that the right half includes fewer data points than the left half. Consequently, higher noise is created in the estimated parameters.
It would be desirable to have an efficient technique to improve PSF model estimation.
BRIEF DESCRIPTION OF THE FIGURES