The H-scan analysis and results in tissues

Abstract

The H-scan is based on a simplified framework for characterizing scattering behavior, and visualizing the results as color coding of the B-scan image. The methodology begins with a standard convolution model of pulse-echo formation from typical situations, and then matches those results to the mathematics of Gaussian Weighted Hermite Functions. The nth successive differentiation of the Gaussian pulse G = exp(-t 2) generates the nth order Hermite polynomial (Poularikas 2010). The function H 4(t)G resembles a broadband pulse. Assuming a pulse-echo system has a round trip impulse response of A 0 H 4(t)G, then we expect that a reflection from a step function of acoustic impedance will produce a corresponding received echo proportional to GH4(t). However, a thin layer of higher impedance, or a small scatterer or incoherent cloud of small scatterers would produce higher order Hermite functions as echoes. In this framework, the identification task is simply to classify echoes by similarity to either GH 4(t), or GH 5(t), or GH 6(t). The resulting B-scan image is examined and echoes can be classified and colored according to their class. Results from tissue scans also demonstrate groups of echoes separated by Hermite order Hn. A theoretical framework is introduced where reflections are characterized by their similarity to nth order Hermite polynomials.