Synthetic aperture imaging using a Lagrange based filtering technique.

Synthetic aperture imaging using a catheter based, circular phased array providing high resolution, dynamic focusing has been explored. Due to the high input impedance and low signal-to-noise ratio (SNR) of a classic single element synthetic aperture system, multi-element synthetic aperture processing has been proposed with SNR improvement of about 8 dB for a 33 element aperture. Reconstruction in this case uses an optimal filtering approach based on minimizing the mean square error between filter output and desired beam pattern. This approach, however, does not directly control both mainlobe beamwidth and sidelobe levels. To overcome this problem, a Lagrange based filter design technique has been developed that not only satisfies the minimum energy criterion, but also constrains sidelobe levels under a certain threshold. The new technique provides better spatial and contrast resolution. Both the mathematical formulation and simulation results are presented.