Linear system models for ultrasonic imaging: application to signal statistics.
Linear equations for modeling echo signals from shift-variant systems forming ultrasonic B-mode, Doppler, and strain images are analyzed and extended. The approach is based on a solution to the homogeneous wave equation for random inhomogeneous media. When the system is shift-variant, the spatial sensitivity function--defined as a spatial weighting function that determines the scattering volume for a fixed point of time--has advantages over the point-spread function traditionally used to analyze ultrasound systems. Spatial sensitivity functions are necessary for determining statistical moments in the context of rigorous image quality assessment, and they are time-reversed copies of point-spread functions for shift variant systems. A criterion is proposed to assess the validity of a local shift-invariance assumption. The analysis reveals realistic situations in which in-phase signals are correlated to the corresponding quadrature signals, which has strong implications for assessing lesion detectability. Also revealed is an opportunity to enhance near- and far-field spatial resolution by matched filtering unfocused beams. The analysis connects several well-known approaches to modeling ultrasonic echo signals.
Zemp
Roger J
RJ
Department of Biomedical Engineering, University of California, Davis, CA 95616, USA.
Abbey
Craig K
CK
Insana
Michael F
MF
D003198:Computer Simulation; D019544:Equipment Failure Analysis / Q000379:methods*; D016014:Linear Models; D008954:Models, Biological; D011786:Quality Control; D015203:Reproducibility of Results; D012542:Scattering, Radiation; D012680:Sensitivity and Specificity; D014463:Ultrasonography / Q000295:instrumentation* / Q000379:methods* / Q000592:standards