Fast Bayesian regularization for vibration elastography

In this work we show that a novel application of Bayesian regularization can be applied as fast, post-processing procedure to vibration elastography reconstructions to reduce artefacts. The technique allows for fast and simple algorithms to be applied as an initial reconstruction provided that both an estimate and its uncertainty are obtained. Bayesian methods work by incorporating prior information from the user. In this case, the operator-supplied a-priori knowledge is the expected feature size in the reconstruction. With this parameter, the algorithm creates a temporary filtered image where each pixel is a weighted average of its neighbors in the initial reconstruction. The variance of these neighbors is also computed and stored. The final image is ten a weighted average of the initial reconstruction with weights being the inverse of the respective variances. The effect it to use the initial reconstruction as the final result whenever its variance is low but when its variance is high to use an average of the surrounding pixels. The entire algorithm (including initial reconstruction using filter ratios) can be implemented in less than 100 lines of (Python) code and takes only a few seconds to run for a 256×256 image on 700 MHz Pentium III machines. We apply the algorithm to simulated vibration elastography data, and real data collected from 5%-20% graphite-laden bovine gels using 400Hz vibrations detected both with a 3.5MHz ultrasound transducer and MRI. The results show that reconstruction artefacts are significantly reduced especially those due to variability in the signal-to-noise ratio of the displacement measurements.