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A new approach to ultrasound imaging with coded-excitation is presented. The imaging is performed by reconstruction of the scatterer strength on an assumed grid covering the region of interest (ROI). Our formulation is based on an assumed discretized signal model which represents the received sampled data vector as a superposition of impulse responses of all scatterers in the ROI. The reconstruction operator is derived from the pseudo-inverse of the linear operator (system matrix) that produces the received data vector. The singular value decomposition (SVD) method with appropriate regularization techniques is used for obtaining a robust realization of the pseudo-inverse. Under simplifying (but realistic) assumptions, the pseudo-inverse operator (PIO) can be implemented using a bank of transversal filters with each filter designed to extract echoes from a specified image line. This approach allows for the simultaneous acquisition of a large number of image lines. This could be useful in increasing frame rates for two-dimensional imaging systems or allowing for real-time implementation of three-dimensional imaging systems. When compared to the matched filtering approach to similar coded-excitation systems, our approach eliminates correlation artifacts that are known to plague such systems. Furthermore, the lateral resolution of the new system can exceed the diffraction limit imposed on conventional imaging systems utilizing delay-and-sum beamformers. The range resolution is compared to that of conventional pulse-echo systems with resolution enhancement (our PIO behaves as a pseudo-inverse Wiener filter in the range direction). Both simulation and experimental verification of these statements are given.