Filter-based compounded delay estimation with application to strain imaging
Ultrasonic wave interference produces local fluctuations in both the envelope, known as speckle, and phase of echoes. Furthermore, such fluctuations are correlated in space, and subsequent motion estimation from the envelope and/or phase signal produces patterned, correlated errors. Compounding, or combining information from multiple decorrelated looks, reduces such effects. We propose using a filter bank to create multiple looks to produce a compounded motion estimate. In particular, filtering in the lateral direction is shown to preserve delay estimation accuracy in the filtered sub-bands while creating decorrelation between sub-bands at the expense of some lateral resolution. For Gaussian apodization, we explicitly compute the induced signal decorrelation produced by Gabor filters. Furthermore, it is shown that lateral filtering is approximately equivalent to steering, in which filtered sub-bands correspond to signals extracted from shifted sub-apertures. Field II simulation of a point spread function verifies this claim. We use phase zero and its variants as displacement estimators for our compounded result. A simplified deformation model is used to provide computer simulations of deforming an elastic phantom. Simulations demonstrate root mean square error (RMSE) reduction in both displacement and strain of the compounded result over conventional and its laterally blurred versions. Then we apply the methods to experimental data using a commercial elastic phantom, demonstrating an improvement in strain SNR.