Di Lai


In reflective ultrasonic imaging, some statistical parameters can be extracted from the backscattered RF signal. Applying Rayleigh statistics or non-Rayleigh statistics to these parameters, the underlying tissue parameters such as effective scatterer number density that characterize the tissues can be further estimated. However, if the statistical processing is applied to the time domain signal, narrow band excitation pulse needs to be used when we consider the frequency dependency of the backscattered signal. The scattering resolution volume is also difficult to estimate. Chen, et al proposed a different method to determine the frequency-dependent effective scatterer number density, which is the actual number density multiplied by a frequency-dependent factor that depends on the differential scattering cross sections of all the scatterers. This method accounts for the possibility that different sets of scatterers may dominate the echo signal at different frequencies. It also avoids the difficulties for estimating the scattering volume. The frequency-dependent effective volume confined by some depth from z1 to z2 need to be evaluated. To evaluate this effective volume, the factors such as the input pulse function, the transducer transfer function, as well as the two-way diffraction effect need to be taken into consideration. The one way diffraction filter is approximated by the closed form Lommel diffraction formulations since the Lommel diffraction formulations and the exact time domain solutions known as 'arccos' form an approximate Fourier transform pair. The advantage of this approximation is that it is valid not only in the focal zone but also in the near field of transducer. In this thesis, an algorithm was designed to numerically calculate the effective volume. We demonstrated how the value of effective volume changes with different time gate weighting functions, different time gate widths, different input pulse bandwidths, as well as the different center locations of the time gate. When the input pulse bandwidth is narrow enough so that the width of pulse can't be ignored when it is compared with the width of time gate, a modified method was proposed to compensate the edge effect. For two types of transducers, the calculation results were compared with the results obtained experimentally by Chen, et al under same conditions. The numerical results prove to be very close to the experimental results. The numerical calculation results obtained were further applied to the post-processing of the experimental echo signal data obtained from fresh pig liver, sponge in water and excised breast tissue samples. The echo signal data was acquired with different bandwidths and 3.5MHz center frequency. For 1.0MHz input pulse bandwidth, the frequency dependent effective scatterer number densities with different analysis time gate lengths were estimated. This analysis often reveals the presence of a coherent phasor sum in the random walk problem, also known as Rician behavior. The frequency dependent behavior was shown for different samples even at a narrow range of frequency around the center frequency. Different methods were used to estimate the statistical parameters by curve fitting either the histogram of the spectrum or the 2nd and higher order spectral moments, including fractional moments. The spectral moments fitting parameters obtained from the Generalized-K distribution model were used in a scatter plot for tissue differentiation.

Library of Congress Subject Headings

Ultrasonic imaging--Mathematical models; Diagnostic ultrasonic imaging; Imaging systems in medicine; Tissues--Examination; Cells

Publication Date


Document Type


Department, Program, or Center

Chester F. Carlson Center for Imaging Science (COS)


Rao, N. A, H. K.


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