Non-Rayleigh statistics of ultrasonic backscattered echoes

Till recently, many of the tissue characterization models have been based on the Rayleigh distribution. However, there have been many instances cited in literature suggesting that deviations from Rayleigh statistics occur when the region of interest contains fewer number of scatterers, exhibits significant variations in scattering cross-section, or contains scatterers with some form of periodic alignment. To account for these non-Rayleigh statistics, new models that are very general and flexible in scope have been proposed in this thesis. The K-distribution is a very general model for characterizing the envelope statistics regardless of whether they are pre-Rayleigh or Rayleigh in nature. In addition, its parameters have the capability for providing relative information on both the number of scatterers as well as the scattering cross-sections simultaneously, in contrast to many of the existing models. Another aspect of non-Rayleigh statistics was also investigated by analyzing the phase information. In the presence of periodic or quasi-periodic scatterers, the phases are no longer uniformly distributed. Two new parameters, the signal to noise ratio of the phase and a [chi]2 test statistic obtained from conducting a [chi]2 goodness of fit test to test the uniformity of the phase distribution, have been introduced to characterize the presence of periodic elements. These two techniques in combination with the power spectral density provide us with a more robust means of identifying the presence of periodic elements. Yet another model, the generalized K-distribution, was developed to characterize scattering from different types of tissues with differing scattering arrangements. This is truly a wide ranging model and it can characterize the whole spectrum of speckle statistics (pre-Rayleigh, Rayleigh or post-Rayleigh distributions). In essence, a novel multi-parametric approach to tissue characterization involving the envelope, phase and the power spectral density has been provided, and these methods would serve as useful tools in the area of tissue characterization. In addition, by combining all these parameters it would be possible to provide a more accurate description of the scattering properties of tissue being imaged.