Optimization of Pinhole SPECT Calibration Dirk Bequ´ e, Johan Nuyts, Guy Bormans, Paul Suetens, and Patrick Dupont Abstract—Previously, we developed a method to determine the acquisition geometry of a pinhole camera. This information is needed for the correct reconstruction of pinhole SPECT images. The method uses a calibration phantom consisting of three point sources. Their positions in the field of view influence the accuracy of the geometry estimate. This study proposes a specific configuration of point sources with a specific position in the field of view for optimal image reconstruction accuracy. For the proposed calibration setup, inaccuracies of the geometry estimate due to noise in the calibration data, only cause sub-resolution inaccuracies in reconstructed images. Further, the calibration method uses a model of the point source configuration, which is only known with limited accuracy. The study demonstrates however, that, with the proposed calibration setup, the error in reconstructed images is comparable to the error in the phantom model. Index Terms— Pinhole, geometric calibration, acquisition geom- etry, SPECT. I. I NTRODUCTION The reconstruction of pinhole SPECT data requires a correct description of the acquisition geometry of the pinhole camera. For a conventional pinhole system with a circular orbit of a plane detector, this geometry can be uniquely described by the seven parameters listed in Table I and extensively discussed in [1]. Previously, we developed a method to determine these parameters from the SPECT acquisition of a calibration phan- tom consisting of three point sources [1]. The method can be considered as an extension of previous methods, estimating a subset of the above parameters, using one [2]–[5] or two [6] point sources. To estimate all 7 parameters, three point sources are necessary and sufficient, and a model of the point source configuration has to be available [1]. For most point source configurations, the knowledge of at least two of the distances between the point sources provides a sufficient model [1]. In the methods practical implementation, all three distances between the point sources are taken into account in the phantom model [1]. The method first acquires a pinhole SPECT scan of the three point sources and calculates the mass centers of their projections. The acquisition geometry is then determined by a least squares fit of estimated point source projection locations to the measured mass centers. Besides the 7 parameters of the acquisition geometry, the positions of the point sources are Work supported by K.U.Leuven grant OT-00/32, F.W.O. grant G.0174.03 and K.U.Leuven grant IDO/02/012. D. Bequ´ e, J. Nuyts and P. Dupont are with the Dept. of Nuclear Medicine, K.U.Leuven, G. Bormans is with the Lab. for Radiopharmaceutical Chemistry, K.U.Leuven, and P. Suetens is with the Lab. for Medical Image Computing, K.U.Leuven. (e-mail: dirk.beque@uz.kuleuven.ac.be) TABLE I PINHOLE PARAMETERS. Symbol Name f Focal length d Distance d m Mechanical offset eu ev Electrical shifts Φ Tilt angle Ψ Twist angle estimated as well, but not the distances between them. This implies that the configuration of the calibration phantom has to be known (to be used as the phantom model), but not its position in the field of view of the camera. With noisy calibration data, the acquisition geometry can only be estimated with limited accuracy. Both the configuration of the calibration phantom and its position in the field of view influence this accuracy. In the remainder of this text, the combination of phantom configuration and phantom position will be referred to as ’calibration setup’. The use of an incorrect phantom model in the calibration calculations can degrade this accuracy even further. During reconstruction, the resulting errors on the acquisition geometry propagate into the reconstructed images, causing loss of spatial resolution and/or image deformation. The aim of this study is to determine the optimal calibration setup for accurate image reconstruction and to study the effect of an incorrect phantom model for this optimal calibration setup. For clarity, table II provides an overview of the different entities involved in the calibration process. II. METHOD First, the propagation of noise on the calibration data to errors on the acquisition geometry is calculated by a linear approach. The propagation of phantom model errors is estimated by simulation. Then the effect on image reconstruction of the resulting estimation errors, due to either noisy data or phantom model errors, is evaluated. A. Estimation Accuracy The projection coordinates U 0 of the three calibration point sources can be calculated analytically in function of the acquisi- tion geometry and the point source locations (calibration setup) [1]. For small variations ΔP in the acquisition geometry and/or phantom position, we assume that the resulting projection coordinates U can also be approximated from the original projections by a linear system U = U 0 + M ΔP. (1)