A Gaussian model approach for the prediction of speckle reduction with spatial and frequency compounding

In the past different analytical expressions have been derived to describe the correlation curve ρ(Δx) of two ultrasonic images which are created from a set of subapertures for spatial compounding or a set of subbands for frequency compounding. We show that both speckle reduction with spatial compounding (SC) and with frequency compounding (FC) can be modeled by a Gaussian shaped correlation curve of the kind ρ(Δx)=exp(-Δx²/α), where Δx represents either the relative shift between neighboring subapertures or neighboring subbands and the parameter α is a constant which describes the inherent properties of the two compounding algorithms. With our experiments the parameter α is estimated individually for SC and FC and the model is used to determine the optimum number of subimages to obtain maximum lesion detectability with a predefined loss in resolution. The results are compared with experimental data