Bayesian and least squares approaches to ultrasonic scatterer size image formation

Scatterer size images can be used to describe renal microstructure and function in vivo. Such information may facilitate early detection of disease processes. When high range resolution is required, however, it is necessary to analyze short data segments. Periodogram-based maximum likelihood (ML) techniques for scatterer size estimation are limited in these situations by noise and range-gate artifacts. Moreover, when the input signal-to-noise ratio (SNR) of the echo signal is small, performance is further degraded. If accurate prior information about the approximate properties of the object is available, it can be incorporated into the solution to improve the estimates by reducing the number of possible solutions. In this paper, use of prior knowledge in scatterer size image formation is investigated. A maximum a posteriori (MAP) estimator, based on a random-object model, and an iterative constrained least squares (CLS) estimator, based on a deterministic-object model, are designed. Their performances and that of a Wiener filter are compared with the ML technique as a function of gate duration and SNR.