Elastogram estimation using adaptive-length Savitzky-Golay digital differentiators

Studies have shown that the Savitzky-Golay digital differentiator (SGDD) is a promising technique in elastography due to its ability in reducing elastogram noises and enhancing the contrast-to-noise ratio between lesion and background tissue. The performance of SGDD is mainly determined by its length/order. Usually, the proper differentiator length is determined as the one providing the maximum contrast between lesions and background tissues. Generally, long SGDDs reduce noise in uniform-strain regions more effectively, and can therefore improve lesion-detection ability. However, they may also lead to bias in regions of abrupt strain changes and finally limit the enhancement to contrast. Therefore, it will be advantageous to determine differentiator length according to local properties of elastograms. In this study, we propose a method to adaptively select proper SGDD length according to local properties of displacement estimates. Simulation experiments show that this method tends to select long SGDDs in regions of uniform strains, and prefers short SGDDs in regions presenting abrupt strain changes. Finally, the limitation to contrast induced by over-smoothing of single length SGDD can be overcome, and further enhancement to contrast is provided.