  Due to its non-invasive and non-radiating nature, along with its low cost,
ultrasound (US) imaging is widely used in medical applications. Typical B-mode
US images have limited resolution and contrast and weak physical
interpretation. Inverse US methods were developed to reconstruct the media's
speed-of-sound (SoS) based on a linear acoustic model. However, the wave
propagation in medical US is governed by nonlinear acoustics, which introduces
more complex behaviors neglected in the linear model. In this work we propose a
nonlinear waveform inversion (NWI) approach for quantitative US, that considers
a nonlinear acoustics model to simultaneously reconstruct multiple material
properties, including the medium's SoS, density, attenuation, and nonlinearity
parameter. We thus broaden current inverse US approaches, such as the full
waveform inversion (FWI) algorithm, by considering nonlinear media, and
additional physical parameters. We represent the nonlinear acoustic model by
means of a recurrent neural network, which enables us to apply advanced
optimization algorithms borrowed from the deep learning toolbox and achieve
more efficient reconstructions compared to the FWI method. We evaluate the
performance of our approach on in-silico data and show that neglecting
nonlinear effects may result in substantial degradation in the reconstruction,
paving the way of NWI into clinical applications.
