Physics-Based Learning of the Wave Speed Landscape in Complex Media

Wave velocity is a key parameter for imaging complex media, but in vivo measurements are typically limited to reflection geometries, where only backscattered echoes from short-scale heterogeneities are accessible. As a result, conventional reflection imaging fails to recover large-scale variations of the wave velocity landscape. Here we show that matrix imaging overcomes this limitation by exploiting the quality of wave focusing as an intrinsic guide star. We model wave propagation as a trainable multi-layer network that leverages optimization and deep learning tools to infer the wave velocity distribution. We validate this approach through ultrasound experiments on tissue-mimicking phantoms and human breast tissues, demonstrating its potential for tumour detection and characterization. Our method is broadly applicable to any kind of waves and media for which a reflection matrix can be measured.