Reflection Matrix Approach for Quantitative Imaging of Scattering Media

Abstract

We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof of concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics for which multielement technology is available. The concept is that focused beam forming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The interelement responses of this virtual array form a focused reflection matrix from which spatial maps of various characteristics of the propagating wave can be retrieved. Here we demonstrate (i) a local focusing criterion that enables the image quality and the wave velocity to be evaluated everywhere inside the medium, including in random speckle, and (ii) a highly resolved spatial mapping of the prevalence of multiple scattering, which constitutes a new and unique contrast for ultrasonic imaging. The approach is demonstrated for a controllable phantom system and for in vivo imaging of the human abdomen. More generally, this matrix approach opens an original and powerful route for quantitative imaging in wave physics.

Alternate abstract:

Plain Language Summary

In medical ultrasound imaging, transducer arrays (collections of small independent sources and receivers) are placed on the outside of the body, with the aim of gathering information about the structure deep inside. Ideally, one would place the sources and receivers closer or inside the organ of interest. However, this is hardly possible for noninvasive imaging. Here, we show that data collected by a commercial medical imaging apparatus can be manipulated to create tiny “virtual” acoustic sources and receivers anywhere inside the human body.

This technique enables us to observe how acoustic waves travel between various areas in a human organ, which we demonstrate for in vivo measurements on the liver. Because the path and speed of acoustic waves is directly related to the structure through which they travel, these observations enable the creation of new 2D images of various organ properties related to their density and composition. These images, in turn, can give valuable insight into the health of the organ tissue.

More broadly, our approach can be extended to any kind of wave that can be controlled by a multielement array. Applications range from biomedical diagnosis in optical imaging to crack detection in industrial materials or monitoring volcanoes and fault zones in geophysics.