Optimal basis for real-time compression of ultrasound rf signals

Modern medical ultrasound machines produce enormous amounts of data, as much as several gigabytes/sec in some systems. The difficulties of generating, propagating and processing such large amounts of data have motivated recent research into means for compression of the radio frequency (rf) signals received at an ultrasound system's analog front end. Most of this work has concentrated on the digitized data available after sampling and A/D conversion. We are interested in the possibility of compression implemented directly on the received analog signals, so we focus on efficient real-time representations for the rf signals comprising a single receive aperture. We first derive an expression for the (time and space) autocorrelation function of the set of signals received in a linear aperture. This is then used to find the autocorrelation's eigenfunctions, which form an optimal basis for minimum mean-square error (mmse) compression of the aperture signal set. Computation of the coefficients of the signal set with respect to the basis amounts to calculation of Fourier Series coefficients for the received signal at each aperture element, with frequencies scaled by aperture position, followed by linear combinations of corresponding frequency components across the aperture. The combination weights at each frequency are determined by the eigenvectors of a matrix whose entries are averaged cross-spectral coefficients of the received signal set at that frequency. The autocorrelation decomposition and signal set coefficients are also used to compute a linear mmse beamformed estimate of the aperture center line.