An optimal image operator design technique for coded excitation ultrasound imaging system

We have recently proposed a new coded excitation ultrasound imaging system. The system is based on a discretized linear model of the received data from the region of interest (ROI). Thus the system can be characterized by a linear equation with operator G consisting of on-grid impulse responses. The image reconstruction is obtained by solving the equation with a pseudo-inverse image operator (PIO). Since the reconstruction quality of the system is determined by the PIO, an effective design method is necessary to find an optimal PIO (i.e., a PIO has small noise sensitivity and the degradation of its performance caused by off-grid scatterers is well below a pre-specified tolerable level). In this report, an optimal PIO design method is presented with the help of singular value decomposition (SVD) technique. Given specifications imposed on the PIO, the proposed design method provides effective procedures for searching a set of suitable system parameters (such as grid size, codes, transmit channels, etc.). Then, the desirable PIO is evaluated by a method based on the SVD rank reduction technique. Simulation results are given to show the efficiency of the proposed PIO design method