Learning the Imaging Model of Speed-of-Sound Reconstruction via a Convolutional Formulation

Speed-of-sound (SoS) is an emerging ultrasound contrast modality, where pulse-echo techniques using conventional transducers offer multiple benefits. For estimating tissue SoS distributions, spatial domain reconstruction from relative speckle shifts between different beamforming sequences is a promising approach. This operates based on a forward model that relates the sought local values of SoS to observed speckle shifts, for which the associated image reconstruction inverse problem is solved. The reconstruction accuracy thus highly depends on the hand-crafted forward imaging model. In this work, we propose to learn the SoS imaging model based on data. We introduce a convolutional formulation of the pulse-echo SoS imaging problem such that the entire field-of-view requires a single unified kernel, the learning of which is then tractable and robust. We present least-squares estimation of such convolutional kernel, which can further be constrained and regularized for numerical stability. In experiments, we show that a forward model learned from k-Wave simulations reduces the contrast error of SoS reconstructions by 38%, compared to a conventional hand-crafted line-based wave-path model. This simulation-learned model generalizes successfully to acquired phantom data, reducing the contrast error compared to the conventional hand-crafted alternative. We successfully demonstrate the feasibility of learning machine-specific kernels as well as one-shot learning from a single image. On in-vivo data of a cancerous breast tumor, the phantom-learned model exhibits an SoS contrast of 34.6m/s, as an impressive improvement over the conventional model contrast of merely 3.4m/s.