Stochastic piecewise linear function fitting with application to ultrasound shear wave imaging

Piecewise linear function fitting is ubiquitous in many signal processing applications. Inspired by an application to shear wave velocity imaging in ultrasound elastography, this paper presents a discrete state-space Markov model for noisy piecewise linear data and also proposes a tractable algorithm for maximum a posteriori estimation of the slope of each segment in the piecewise linear function. The number and locations of breaks is handled indirectly by the stochastics of the Markov model. In the ultrasound shear wave imaging application, these slope values have concrete physical interpretation as being the reciprocal of the shear wave velocities in the imaged medium. Data acquired on an ellipsoidal inclusion phantom shows that this algorithm can provide good contrast of around 6 dB and contrast to noise ratio of 25 dB between the stiff inclusion and surrounding soft background. The phantom validation study also shows that this algorithm can be used to preserve sharp boundary details, which would otherwise be blurred out if a sliding window least squares filter is applied.