[Paper Review] Physics-Based Learning of the Wave Speed Landscape in Complex Media

Baptiste Hériard-Dubreuil, Emma Brenner+5 more|arXiv (Cornell University)|Feb 3, 2026

Ultrasound Imaging and Elastography0 citations

TL;DR

The paper presents a learning-based matrix imaging framework that uses a differentiable forward model to infer the wave speed distribution from reflection data, enabling quantitative speed-of-sound imaging in reflection geometry across ultrasound applications.

ABSTRACT

Wave velocity is a key parameter for imaging complex media, but in vivo measurements are typically limited to reflection geometries, where only backscattered waves 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.

Motivation & Objective

• Motivate quantitative wave-speed imaging in media where large-scale velocity variations are hidden in reflection data.
• Develop a learning-based, differentiable forward model to infer velocity landscapes from reflection matrices.
• Demonstrate speed-of-sound imaging in tissue-mimicking phantoms, ex vivo tissues, and human breast data using ultrasound.
• Show the framework's generality to other wave modalities that provide a reflection matrix.

Proposed method

• Represent wave propagation as a differentiable multi-layer network of cascaded diffraction phase screens interleaved with free-space propagation.
• Use a gradient-based optimization to maximize a focusing quality metric that leverages the reflection matrix data as a guide star.
• Compute the gradient of focusing quality with respect to the velocity model via chain rule and update the velocity map accordingly.
• Employ total-variation regularization, spatial filtering, and other optimization techniques to stabilize convergence.
• Implement the forward model with a split-step Fourier method (beam propagation) to capture forward multiple scattering.
• Ground the approach in matrix imaging by constructing focused reflection matrices and using their diagonal/confinement properties for velocity inference.

Experimental results

Research questions

• RQ1 Can the focusing quality metric derived from focused reflection matrices be used to recover large-scale wave velocity variations from reflection data?
• RQ2 How can a differentiable forward model of wave propagation be constructed to enable gradient-based optimization for velocity landscape estimation?
• RQ3 What limits exist for speed-of-sound reconstruction in reflection geometry, and how can aberrations be mitigated?
• RQ4 Is the approach transferable across ultrasound experiments and potentially to other wave modalities that provide a reflection matrix?

Key findings

• Demonstrates quantitative speed-of-sound imaging in reflection geometry using ultrasound on phantoms, ex vivo tissues, and human breast data.
• Shows improved reflection imaging and restoration of diffraction-limited focusing after velocity correction, with recoveries of ~100 m/s contrasts in phantoms.
• Validates that a gradient-ascent of a physics-inspired focusing-quality metric can recover the velocity landscape without relying on short-scale disorder knowledge.
• Extends the framework to 3D imaging, distinguishing fat and muscle in pork tissue and aligning horizontal slices with known tissue distributions.
• Provides evidence that sound-speed maps can aid lesion differentiation in breast imaging, potentially improving diagnostic performance over conventional B-mode imaging.