Quantitative Accuracy Assessment and Optimization of SPECT Geometrical Calibration

Accurate geometrical calibration is critical to obtaining high resolution and artifact free reconstructed images for modern animal single photon emission computed tomography （SPECT） systems. Although there have been many published works on the calibration of various SPECT systems, few studies have been done to evaluate the efficacy of the proposed calibration methods in a quantitative manner. This paper presents a numerical method to assess both the uniqueness and the quantitative accuracy of SPECT calibration, which is based on analyzing the singular value decomposition （SVD） components of the Jacobian matrix from a least-square cost function of the calibration. The proposed method is firstly validated by applying it to the calibration of a single pinhole SPECT system and comparing the results with those derived using a published method, and is then used to optimize the calibration setup for a slit-slat SPECT system. With the proposed method, a minimum required number of point source projections to achieve the desired calibration accuracy can be estimated and used as figure-of-merit to evaluate the goodness of a calibration setup. An inverse-square relationship between the calibration accuracy and the number of sampled projections is revealed. Optimal calibration setup is determined through an exhaustive search among all the pos- sibilities of point source arrangements under certain conditions. We demonstrate that for the studied system, the best calibration accuracy is achieved by arranging the point source over the edge of FOV with evenly- spaced angular positions. Point source experiments were conducted to validate the proposed method.

A modified interval subdividing based geometric calibration method for interior tomography

The interior tomography is commonly met in practice, whereas the self-calibration method for geometric parameters remains far from explored. To determine the geometry of interior tomography, a modified interval subdividing based method, which was originally developed by Tan et al.,^[11] was presented in this paper. For the self-calibration method, it is necessary to obtain the reconstructed image with only geometric artifacts. Therefore, truncation artifacts reduction is a key problem for the self-calibration method of an interior tomography. In the method, an interior reconstruction algorithm instead of the Feldkamp-Davis-Kress （FDK） algorithm was employed for truncation artifact reduction. Moreover, the concept of a minimum interval was defined as the stop criterion of subdividing to ensure the geometric parameters are determined nicely. The results of numerical simulation demonstrated that our method could provide a solution to the self- calibration for interior tomography while the original interval subdividing based method could not. Furthermore, real data experiment results showed that our method could significantly suppress geometric artifacts and obtain high quality images for interior tomography with less imaging cost and faster speed compared with the traditional geometric calibration method with a dedicated calibration phantom.

Geometric Calibration and Image Quality Assessment of High Resolution Dual-Camera Satellite

The evaluation of geometric calibration accuracy of high resolution satellite images has been increasingly recognized in recent years.In order to evaluate geometric accuracy for dual-camera satellite images based on the ground control points(GCP),a rigorous geometric imaging model,which was based on the collinear equation of the probe directional angle and the optimized tri-axial attitude determination(TRIAD)algorithm,is presented.Two reliable test fields in Tianjin and Jinan(China)were utilized for geometric accuracy validation of Pakistan Remote Sensing Satellite-1.The experimental results demonstrate a certain deviation of the on-orbit calibration result from the initial design values of the calibration parameters.Therefore,on-orbit geometric calibration is necessary for optical satellite imagery.Within this research,the geometrical performances including positioning accuracy without/with GCP and band registration of the dual-camera satellite were analyzed in detail,and the results of geometric image quality are assessed and discussed.As a result,it is feasible and necessary to establish such a geometric calibration model to evaluate the geometric quality of dual-camera satellite.

On-orbit Geometric Calibration and Preliminary Accuracy Evaluation of GF-14 Satellite

GF-14 satellite is a new generation of sub-meter stereo surveying and mapping satellite in China,carrying dual-line array stereo mapping cameras to achieve 1∶10000 scale topographic mapping without Ground Control Points(GCPs).In fact,space-based high-precision mapping without GCPs is a challenging task that depends on the close cooperation of several payloads and links,of which on-orbit geometric calibration is one of the most critical links.In this paper,the on-orbit geometric calibration of the dual-line array cameras of GF-14 satellite was performed using the control points collected in the high-precision digital calibration field,and the calibration parameters of the dual-line array cameras were solved as a whole by alternate iterations of forward and backward intersection.On this basis,the location accuracy of the stereo images using the calibration parameters was preliminarily evaluated by using several test fields around the world.The evaluation result shows that the direct forward intersection accuracy of GF-14 satellite images without GCPs after on-orbit geometric calibration reaches 2.34 meters(RMS)in plane and 1.97 meters(RMS)in elevation.

Preliminary Pointing Bias Calibration of ZY3-03 Laser Altimeter

ZiYuan3-03(ZY3-03)satellite was launched on July 25,2020,equipped with China’s second-generation laser altimeter for earth observation.In order to preliminarily evaluate the in-orbit performance of the ZY3-03 laser altimeter,the pointing bias calibration based on terrain matching method was adopted.Three tracks of laser data were employed for the ZY3-03 laser altimeter calibration test.Three groups of pointing parameters were obtained respectively,and the mean value of pointing is considered as the optimal calibration result.After calibration,ZY3-03 laser pointing accuracy is greatly improved by the method,and its pointing accuracy is approximately 12.7 arcsec.The first-track laser data on the Black Sea surface is used to evaluate the relative elevation accuracy of ZY3-03 laser altimeter after pointing bias calibration,which is improved from 0.33 m to 0.19 m after calibration.Meanwhile,the absolute elevation accuracy of ZY3-03 laser altimeter after pointing bias calibration is evaluated by the Ground Control Points(GCPs)measured by RTK(Real-Time Kinematic),which is better than 0.5 m in the flat terrain.

Accuracy enhancement of the spherical actuator with a two-level geometric calibration method

This paper presents a two-level geometric calibration method for the permanent magnet （PM） spherical actuator to improve its motion control accuracy. The proposed actuator is com- posed of a stator with circumferential coils and a rotor with multiple PM poles. Due to the assembly and fabrication errors, the real geometric parameters of the actuator will deviate from their design values. Hence, the identification of such errors is critical for the motion control tasks. A two-level geometric calibration approach is proposed to identify such errors. In the first level, the calibration model is formulated based on the differential form of the kinematic equation, which is to identify the geometric errors in the spherical joint. In the second level, the calibration model is formulated based on the differential form of torque formula, which is to calibrate the geometric parameters of the magnetization axes of PM poles and coils axes. To demonstrate the robustness and availability of the calibration algorithm, simulations are conducted. The results have shown that the proposed two-level calibration method can effectively compensate the geometric parameter errors and improve the positioning accuracy of the spherical actuator.

Geometric calibration for a SPECT system dedicated to breast imaging

Geometric calibration is critical to the accurate SPECT reconstruction. In this paper, a geometric calibration method was developed for a dedicated breast SPECT system with a tilted parallel beam （TPB） orbit. The acquisition geometry of the breast SPECT was firstly characterized. And then its projection model was established based on the acquisition geometry. Finally, the calibration results were obtained using a nonlinear optimization method that fitted the measured projections to the model. Monte Carlo data of the breast SPECT were used to verify the calibration method. Simulation results showed that the geometric parameters with reasonable accuracy could be obtained by the proposed method.

A new method to determine the projected coordinate origin of a cone-beam CT system using elliptical projection

In order to determine the projected coordinate origin in the cone-beam CT scanning system with respect to the Feldkamp-Davis-Kress （FDK） algorithm, we propose a simple yet feasible method to accurately measure the projected coordinate origin. This method was established on the basis of the theory that the projection of a spherical object in the cone-beam field is an ellipse. We first utilized image processing and the least square estimation method to get each major axis of the elliptical Digital Radiography （DR） projections of a group of spherical objects. Then we determined the intersection point of the group of major axis by solving an over-determined equation set that was composed by the major axis equations of all the elliptical projections. Based on the experimental results, this new method was proved to be easy to implement in practical scanning systems with high accuracy and anti-noise capability.