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Should compression of coded waveforms be done before or after focusing?

In medical ultrasound signal-to-noise ratio improvements of approximately 15-20 dB can be achieved by using coded waveforms. Exciting the transducer with an encoded waveform necessitates compression of the response which is computationally demanding. This paper investigates the possibility of reducing the workload without introducing errors. Ne - 1 compression filtrations (convolutions) can be saved by inverting the precedence of compression and beamforming (called post-compression), when N is the number of transducer elements. Post-compression with dynamic receive focusing will theoretically introduce errors. Simulations and measurements show that increasing the depth of the scatterers results in a decreased error. Transmit focus depth and the distance between focus points have a significant influence on the error. The size of the error is studied and a new scheme for correcting the error is proposed. The study is done by simulations in Field II and by measurements with our experimental scanner RASMUS. The measurements are done on a string phantom and in-vivo on the abdomen of a male volunteer.