Linear prediction filtering of per channel data for noise reduction - theory of action and application to cardiac ultrasound

Cardiac ultrasound imaging suffers from acoustic artefacts including diffraction limitation, aberration, reverberation, multipath, and electronic noise. In particular, multipath through the chest wall gives rise to a diffuse haze that obscures clinically relevant features. Linear prediction filtering applied to time-aligned array channel data has recently been introduced for white noise reduction in ultrasound. Our objectives in this work are 1) theoretical: to summarize the insights underpinning linear prediction filtering of array data thereby providing a mathematical framework to analyze its effects; and 2) experimental: to test the effectiveness of this technique in reducing multipath noise that produces diffuse cardiac haze. A signal model of array data originating from a superposition of far-field point sources can be expressed with a fully deterministic recursion and interpreted as a linear prediction model. The linear prediction filter is the minimum mean square error estimator of the predictable signal components. Linear prediction filtering is equivalent to applying a spatial filter to the channel data prior to beam-sum. The filter, combined to beamsumming, is equivalent to a applying a post-filter (i.e. mask) to the beam-summed data, whose amplitude is the DC response of the filter. Linear prediction filtering was applied on in-vivo cardiac datasets and compared to applying a Wiener postfilter designed to minimize the mean squared error of the beamformed output in the presence of white noise. Compared to Wiener filtering, the linear prediction filter was effective at reducing chamber haze levels, but it preserved sidelobe signals. The linear prediction framework may reduce scattering from structures of interest if the signal to interference ratio is low.