Generation of synthetic-focus images from pulse-echo ultrasound using difference equations

To produce a complete-dataset, pulse-echo image requires a knowledge of the time of flight (TOF) from each source to each sensor in the transducer array for each site to be imaged. Increasing the speed of TOF calculation is important in adaptive-focus schemes. The authors determined TOF more rapidly than via direct calculation by representing TOF surfaces by two-dimensional (2-D), positive-integer-degree polynomials implemented in their forward-difference form. Errors which accumulate due to the use of a difference equation depend on the degree of the polynomial and on the size of the image. The number of bits needed to address echo samples in backscatter memory and the allowable error define the minimum precision needed for accurate values of TOF, Accurate calculation of TOF, expressed as 10-b addresses in backscatter memory, for each pixel in a 512x512 image with a second-degree difference equation requires 44 b of precision, Using the complete dataset from a 32-element array and a second-degree approximation to TOF on a typical graphics workstation reduced generation time of a 512x512 image from 702 to 239 s. Parallel formulation of both the TOF calculation and the retrieval and summation of echo samples resulted in significant further reduction in image-generation time. Parallel implementation on a SIMD array with 4096 processors, each of which had an indirect-addressing mode, allowed the generation of a 512x512 image in 16.3 s.