A new coded-excitation ultrasound imaging system. II. Operator design

For pt.I see ibid. vol.43, pp.131-140 (1996). We introduced in pt. I a new approach for ultrasonic imaging using coded-excitation. Our formulation allows for the implementation of the imaging operator as a transversal filter bank with each filter designed to reconstruct scatterer distribution along one image line. This formulation allows for high-speed data acquisition when the reconstruction filters are utilized in parallel configuration. Furthermore, under high signal-to-noise ratio (SNR) conditions, our approach allows for spatial resolution that exceeds the resolution set by the diffraction limit. Ideally, the resolution limit for our system is set by the grid spacing in the region of interest (ROI). When the SNR of the system is finite, however, sensitivity to noise becomes a factor in image reconstruction quality. A trade-off exists between spatial and contrast resolutions with all elements of this trade-off captured by the singular value decomposition (SVD) of the imaging operator, G. In this paper, we demonstrate the use of the function given in pt.I in defining an optimal pseudo-inverse operator (PIO). The optimal PIO provides the highest spatial resolution at which the mean-square error (MSE) is minimized. We show that a design procedure for such an optimal image reconstruction operator is feasible, and we present an algorithm for operator design. Computer simulations are used to highlight the main features of the SVD-based operator design procedure; the SVD of the imaging operator consists of array-dependent (analytic) and code-dependent (nonanalytic) modes. The analytic modes yield a sine-like lateral point spread function (LPSF) of the imaging system. For a given SNR of the imaging system, a maximum number of modes (analytic and nonanalytic) can be used in the design of the imaging operator to minimize the LPSF width (i.e., maximize resolution) while minimizing the MSE. Finally, a two-dimensional cyst simulation is provided to demonstrate the potential advantage of our approach.