Optimized design of CORDIC algorithm for coordinate conversion of medical ultrasonic image

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 re-calibrated 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 result, 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 0.0063 rad to 0.0005 rad and the error of polar radius is suppressed from 0.082 to 0.03.