Simulation of ultrasound image data by a quadrature method

Full text: Simulation is an important step in the process of developing reliable and accurate methods for medical image segmentation. Ultrasound data available from commercial scanners is most easily obtained in envelope detected form. Although bandpass and quadrature data is available it is not clear whether data in these forms would improve segmentation. Previous work (Bamber JC and Dickinson RJ, Phys Med Biol 25,3:463-479,1980) has simulated ultrasound data in bandpass (RF) form, requiring a high sampling rate and large data sets. We present a method for simulation of medical ultrasound images which produces data in quadrature form. The quadrature form allows a lower sampling rate which is dependent only on transducer bandwidth and is independent of centre frequency. We consider a two dimensional ultrasound data set Ib(x, z) where x and z denote lateral and axial spatial coordinates and let Ib(x, z) be bandpass in the axial direction. We then use a quadrature representation: Ib(x, z) = Re[Ic(x, z) expjk0z], where Ic(x, z) = Ip(x, z) + jIq(x, z), and Ip and Iq are (low-pass) quadrature components. We derive an expression for the power spectral density of Ic and from this deduce expressions for the magnitude and phase of the Fourier transform of Ip and Iq. Taking the inverse Fourier transform then yields the simulated data sets Ip and Iq. The above quadrature simulation method has been implemented in a MATLAB like environment. We have demonstrated it to be a simple method for simulation of medical ultrasound images in a quadrature form. The method is essentially the same as previous work however produces quadrature data directly and provides a manageable data set independent of transducer centre frequency