On the statistics of ultrasonic spectral parameters

Several factors affect the accuracy and precision of ultrasonic spectrum analysis, which is used for characterization of normal and diseased tissue in a variety of organs. For example, averaging procedures and the sequence of operations affect the accuracy and precision of spectrum analysis. Averaging procedures and logarithmic conversion (i.e., conversion to dB) introduce a constant bias that affects spectral amplitudes and the values of intercept and midband fit; the bias depends on the sequencing of the log conversion and averaging as well as the number of independent spectra or spectral parameters that are averaged. We derive expressions that permit correction of such biases. Furthermore, we show that standard deviations for slope and midband-fit estimation can be minimized by averaging spectra before dB conversion and before computing spectral parameters by linear regression. Experimental results using phantoms agree remarkably with theoretical predictions for the data window functions studied in this article, Hamming and rectangular.