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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 improves the median contrast of SoS reconstructions by 63%, compared to a conventional hand-crafted line-based wave-path model. This simulation-learned model generalizes successfully to acquired phantom data, nearly doubling the SoS contrast compared to the conventional hand-crafted alternative. We demonstrate equipment-specific and small-data regime feasibility by learning a forward model from a single phantom image, where our learned model quadruples the SoS contrast compared to the conventional hand-crafted model. On in-vivo data, the simulation- and phantom-learned models respectively exhibit impressive 7 and 10 folds contrast improvements over the conventional model.

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