Shape estimation of flexible ultrasound arrays using spatial coherence: A preliminary study

A flexible ultrasound array can potentially provide a larger field-of-view, enhanced imaging resolution, and less operator dependency compared to conventional rigid transducer arrays. However, such transducer arrays require information about relative element positions for beamforming and reconstructing geometrically accurate sonograms. In this study, we assess the potential utility of using spatial coherence of backscattered radiofrequency data to estimate transducer array shape (inverse problem). The methodology is evaluated through 1) simulation of flexible arrays and 2) blinded in vivo experiments using commercial rigid transducer arrays on various anatomical targets (shoulder, forearm, scapular, posterior calf muscles, and abdomen) and multi-purpose ultrasound phantoms. The average Euclidean error of shape estimation is below 0.1 wavelengths for simulated arrays and below 1.4 wavelengths (median: 0.58 wavelengths) for real arrays. The complex wavelet structural similarity index between the B-mode images reconstructed with estimated and ground truth array shapes is above 99 % and 96 %, for simulations and experiments, respectively. These findings suggest that optimizing for spatial coherence may be an effective way to estimate the unknown shape of conformal ultrasound arrays.