A novel algorithm for high-speed parallel processing of ultrasound pulse-echo data for real-time 3-D imaging will be presented. The approach utilizes a discretized model of the received data from the region of interest (ROI) using a conventional beamformer. The transmitter array elements are fed with binary codes designed to produce distinct impulse responses from different directions in ROI. The discretization of the model leads to a matrix operator that can be inverted using a regularized pseudoinverse. Under realistic simplifying assumptions, the pseudoinverse leads to a transversal filter bank with every filter in the bank designed to extract echoes from a specific direction in ROI. The number of filters in the bank determines the number of image lines acquired simultaneously. Experimental results have shown that the new approach is valid for phased array pulse-echo imaging of speckle generating phantoms typically used in characterizing medical imaging systems. Furthermore, it was demonstrated that the new approach has lateral resolution exceeding that of conventional imaging with the same array. A full description of the algorithm along with representative image reconstructions will be given. In addition, operator design criteria for optimal design for SONAR, NDE, and medical imaging will be discussed.