面向医学超声图像坐标变换的CORDIC算法优化

Optimized Design of CORDIC Algorithm for Coordinate Conversion of Medical Ultrasonic Image

本文提出一种用于医学超声内窥成像坐标变换的改进坐标标定的CORDIC(MCC-CORDIC)算法.在传统CORDIC算法的基础上,重新标定直角坐标,同时通过简单的数学转换将坐标位置映射到第1象限后进行坐标变换,减少FPGA资源使用量的同时解决了算法在[0,360°]范围内收敛角度范围不足的问题;通过对数据位宽、模校正方法的优化,提高了算法的精度;基于流水线结构的硬件实现使算法满足超声实时成像的要求.经仿真与超声实时成像实验验证,极角误差由0.006 3 rad减小到0.000 5 rad,极径误差由0.082减小到0.03.

The modified coordinate calibration coordinate rotation digital computer （MCC-CORDIC） algorithm for coordinate conversion was introduced into medical ultrasonic endoscopic imaging system in this paper. Based on the conventional CORDIC algorithm, the Cartesian coordinates were recalibrated to save logic element resources of FPGA. Before coordinate conversion was started, each Cartesian coordinate was mapped onto the first quadrant by a simple mathematical transformation. As a resutt, the problem that the convergence angle range of CORDIC algorithm could not fully cover the range of [0,360°], was solved. The bit width of data and the method of scale factor correction were optimized, so as to improve the accuracy of the algorithm. The MCC-CORDIC algorithm was implemented on FPGA with a pipeline structure, which made the algorithm meet the real-time requirement of ultrasonic imaging system. The MCC-CORDIC algorithm was validated by both simulation and real-time ultrasonic imaging experiment on FPGA. The results show that the error of polar angle is suppressed from 0. 006 3 rad to 0. 000 5 rad and the error of polar radius is suppressed from 0. 082 to 0. 03.