Learnt correction for regularization-related biases in pulse-echo speed-of-sound imaging

Computed ultrasound tomography in echo-mode (CUTE) generates spatially resolved maps of speed of sound (cSoS) based on the shift of echoes detected under varying steering angles. The inversion of SoS from echo shift typically uses 1
^st
order Tikhonov regularization (TR) to constrain the SoS to smooth solutions. In this paper we show in a large-scale simulation study that (a) the resulting SoS maps contain biases compared to the ground truth that depend on the tissue layer geometry; (b) these biases can be substantially reduced by a regularization that minimizes reconstruction errors for a probabilistic distribution of sample properties as opposed to a naïve smoothness constraint. In preparation for a shallow-learning based SoS reconstruction framework, we implement a single-layer artificial neural network (NN) with linear activation function (a linear operator) that is iteratively trained to correct the TR result. We demonstrate that the achieved improvement is optimum by comparison to a one-step derivation of the linear operator based on classical matrix regularization. Our results give confidence in further pursuing the route of shallow learning with potential to account also for non-linear effects by adding more layers while staying real time due to the low computational cost of shallow NNs.