Experimental validation of a convolution- based ultrasound image formation model using a planar arrangement of micrometer-scale scatterers

The shift-invariant convolution model of ultrasound is widely used in the literature, for instance to generate fast simulations of ultrasound images. However, comparison of the resulting simulations with experiments is either qualitative or based on aggregate descriptors such as envelope statistics or spectral components. In the current work, a planar arrangement of 49-μm polystyrene microspheres was imaged using macrophotography and a 4.7-MHz ultrasound linear array. The macrophotograph allowed estimation of the scattering function (SF) necessary for simulations. Using the coefficient of determination R² between real and simulated ultrasound images, different estimates of the SF and point spread function (PSF) were tested. All estimates of the SF performed similarly, whereas the best estimate of the PSF was obtained by Hanningwindowing the deconvolution of the real ultrasound image with the SF: this yielded R² = 0.43 for the raw simulated image and R² = 0.65 for the envelope-detected ultrasound image. R² was highly dependent on microsphere concentration, with values of up to 0.99 for regions with scatterers. The results validate the use of the shift-invariant convolution model for the realistic simulation of ultrasound images. However, care needs to be taken in experiments to reduce the relative effects of other sources of scattering such as from multiple reflections, either by increasing the concentration of imaged scatterers or by more careful experimental design.