  Focusing waves inside inhomogeneous media is a fundamental problem for
imaging. Spatial variations of wave velocity can strongly distort propagating
wavefronts and degrade image quality. Adaptive focusing can compensate for such
aberration, but is only effective over a restricted field of view. Here, we
introduce a full-field approach to wave imaging based on the concept of the
distortion matrix. This operator essentially connects any focal point inside
the medium with the distortion that a wavefront, emitted from that point,
experiences due to heterogeneities. A time-reversal analysis of the distortion
matrix enables the estimation of the transmission matrix that links each sensor
and image voxel. Phase aberrations can then be unscrambled for any point,
providing a full-field image of the medium with diffraction-limited resolution.
Importantly, this process is particularly efficient in random scattering media,
where traditional approaches such as adaptive focusing fail. Here, we first
present an experimental proof-of-concept on a tissue mimicking phantom, and
then apply the method to in vivo imaging of human soft tissues. While
introduced here in the context of acoustics, this approach can also be extended
to optical microscopy, radar or seismic imaging.
