# Training Variational Networks with Multi-Domain Simulations: Speed-of-Sound Image Reconstruction

arXiv: https://arxiv.org/abs/2006.14395 · HTML: https://mlsanity.com/paper/2006.14395/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [Investigating Pulse-Echo Sound Speed Estimation in Breast Ultrasound with Deep Learning](https://mlsanity.com/paper/2302.03064/) (2023)
- [Deep Learning for Ultrasound Speed-of-Sound Reconstruction: Impacts of Training Data Diversity on Stability and Robustness](https://mlsanity.com/paper/2202.01208/) (2022)
- [Ultrasound Signal Processing: From Models to Deep Learning](https://mlsanity.com/paper/2204.04466/) (2022)
- [Uncertainty Estimation for Trust Attribution to Speed-of-Sound Reconstruction with Variational Networks](https://mlsanity.com/paper/2504.11307/) (2025)
- [IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data](https://mlsanity.com/paper/2607.22351/) (2026)

## Abstract (arXiv)

Speed-of-sound has been shown as a potential biomarker for breast cancer imaging, successfully differentiating malignant tumors from benign ones. Speed-of-sound images can be reconstructed from time-of-flight measurements from ultrasound images acquired using conventional handheld ultrasound transducers. Variational Networks (VN) have recently been shown to be a potential learning-based approach for optimizing inverse problems in image reconstruction. Despite earlier promising results, these methods however do not generalize well from simulated to acquired data, due to the domain shift. In this work, we present for the first time a VN solution for a pulse-echo SoS image reconstruction problem using diverging waves with conventional transducers and single-sided tissue access. This is made possible by incorporating simulations with varying complexity into training. We use loop unrolling of gradient descent with momentum, with an exponentially weighted loss of outputs at each unrolled iteration in order to regularize training. We learn norms as activation functions regularized to have smooth forms for robustness to input distribution variations. We evaluate reconstruction quality on ray-based and full-wave simulations as well as on tissue-mimicking phantom data, in comparison to a classical iterative (L-BFGS) optimization of this image reconstruction problem. We show that the proposed regularization techniques combined with multi-source domain training yield substantial improvements in the domain adaptation capabilities of VN, reducing median RMSE by 54% on a wave-based simulation dataset compared to the baseline VN. We also show that on data acquired from a tissue-mimicking breast phantom the proposed VN provides improved reconstruction in 12 milliseconds.