An analytical comparison of ultrasonic array imaging algorithms.

In the paper different techniques for post-processing data from an ultrasonic transducer array are considered. First, a mathematical model of the transmit-receive array data is developed. Then based on this model three imaging methods are formulated: the total focusing method, the wavenumber algorithm, and the back-propagation method. Although these methods are conceptually different and use different approximations they can all be expressed in the form of a linear superposition of transmit-receive signals in the frequency domain with some focusing coefficients. The equivalent coefficients for each processing algorithm are derived, and difference between approaches is discussed. It is shown that in the general case the most appropriate imaging method is the back-propagation method, which is based on the back-propagation of the angular spectrum of transmit-receive signals. The relative performance of the imaging methods is illustrated using simulated and experimental data.