Speed-of-sound is a biomechanical property for quantitative tissue differentiation, with great potential as a new ultrasound-based image modality. A conventional ultrasound array transducer can be used together with an acoustic mirror, or so-called reflector, to reconstruct sound-speed images from time-of-flight measurements to the reflector collected between transducer element pairs, which constitutes a challenging problem of limited-angle computed tomography. For this problem, we herein present a variational network based image reconstruction architecture that is based on optimization loop unrolling, and provide an efficient training protocol of this network architecture on fully synthetic inclusion data. Our results indicate that the learned model presents good generalization ability, being able to reconstruct images with significantly different statistics compared to the training set. Complex inclusion geometries were shown to be successfully reconstructed, also improving over the prior-art by 23% in reconstruction error and by 10% in contrast on synthetic data. In a phantom study, we demonstrated the detection of multiple inclusions that were not distinguishable by prior-art reconstruction, meanwhile improving the contrast by 27% for a stiff inclusion and by 219% for a soft inclusion. Our reconstruction algorithm takes approximately 10 ms, enabling its use as a real-time imaging method on an ultrasound machine, for which we are demonstrating an example preliminary setup herein.