A Spatial Coherence Approach to Minimum Variance Beamforming for Plane-Wave Compounding

A new approach to implement minimum variance distortionless response (MVDR) beamforming is introduced for coherent plane-wave compounding (CPWC). MVDR requires the covariance matrix of the incoming signal to be estimated and a spatial smoothing approximation is usually adopted to prevent this calculation from being underconstrained. In the new approach, we analyze MVDR as a spatial filter that decorrelates signals received at individual channels before summation. Based on the analysis, we develop two MVDR beamformers without using any spatial smoothing. First, MVDR weights are applied to the received signals after accumulating the data over transmits at different angles, while the second involves weighting the data collected in individual transmits and compounding over the transducer elements. In both cases, the covariance matrix is estimated using a set of slightly different combinations of the echo data. We show the sufficient statistic for this estimation that can be described by approximating the correlation among the backscattered ultrasound signals to their spatial coherence. Using the van Cittert-Zernike theorem, their statistical similarity is assessed by relating the spatial coherence to the profile of the source intensity. Both spatial-coherence-based MVDR beamformers are evaluated on data sets acquired from simulation, phantom, and in vivo studies. Imaging results show that they offer improvements over simple coherent compounding in terms of spatial and contrast resolutions. They also outperform other existing MVDR-based methods in the literature that are applied to CPWC.