We present a full-waveform inversion (FWI) of an in-vivo data set acquired with a transmission-reflection optoacoustic ultrasound imaging platform containing a cross-sectional slice through a mouse. FWI is a high-resolution reconstruction method that provides quantitative images of tissue properties such as the speed of sound. As an iterative data-fitting procedure, FWI relies on the ability to accurately predict the physics of wave propagation in heterogeneous media to account for the non-linear relationship between the ultrasonic wavefield and the tissue properties. A key component to accurately predict the ultrasonic field numerically is a precise knowledge of the source characteristics. For realistic problems, however, the source-time function is generally unknown, which necessitates an auxiliary inversion that recovers the time series for each transducer. This study presents an updated sound speed reconstruction of a cross-section through a mouse using source wavelets that are inverted individually per transducer. These source wavelets have been estimated from a set of observed data by application of a source-wavelet correction filter, which is equivalent to a water-level deconvolution. Compared to previous results, the spatial resolution of anatomical features such as the vertebral column is increased whilst artefacts are suppressed.
Full-waveform inversion (FWI) for ultrasound computed tomography is an advanced method to provide quantitative and high-resolution images of tissue properties. Two main reasons hindering the widespread adoption of FWI in clinical practice are (1) its high computational cost and (2) the requirement of a good initial model to mitigate the non-convexity of the inverse problem. The latter is commonly referred to as “cycle-skipping", which occurs for phase differences between synthetic and observed signals and usually traps the inversion in a local minimum. Source-encoding strategies, which simultaneously activate several emitters and have been proposed to reduce the simulation cost, further contribute to this issue due to the multiple arrivals of the wavefronts. We present a time-domain acoustic full-waveform inversion strategy utilizing a recently proposed misfit functional based on optimal transport. Using a graph-space formulation, the discrepancy between simulated and observed signals can be computed efficiently by solving an auxiliary linear program. This approach alleviates the common need for either a good initial model and / or low-frequency data. Furthermore, combining this misfit functional with random source-encoding and a stochastic trust-region method significantly reduces the computational cost per FWI iteration. In-silico examples using a numerical phantom for breast screening ultrasound tomography demonstrate the ability of the proposed inversion strategy to converge to the ground truth even when starting from a weak prior and cycle-skipped data.
Characterizing the spatial resolution and uncertainties related to a tomographic reconstruction are crucial to assess its quality and to assist with the decision-making process. Bayesian inference provides a general framework to compute conditional probability density functions of the model space. However, analytic expressions and closed-form solutions for the posterior probability density are limited to linear inverse problems such as straight- ray tomography under the assumption of a Gaussian prior and data noise. Resolution analysis and uncertainty quantification is significantly more complicated for non-linear inverse problems such as full-waveform inversion (FWI), and sampling-based approaches such as Markov-Chain Monte-Carlo are often impractical because of their tremendous computational cost. However, under the assumption of Gaussian priors in model and data space, we can exploit the machinery of linear resolution analysis and find a Gaussian approximation of the posterior probability density by using the Hessian of the regularized objective functional. This non-linear resolution analysis rests on (i) a quadratic approximation of the misfit functional in the vicinity of an optimal model; (ii) the idea that an approximation of the Hessian can be built efficiently by gradient information from a set of perturbed models around the optimal model. The inverse of the preconditioned Hessian serves as a proxy of the posterior covariance from which space-dependent uncertainties as well as correlations between parameters and inter-parameter trade-offs can be extracted. Moreover, the framework proposed here also allows for inter- comparison between different tomographic techniques. Specifically, we aim for a comparison between tissue models obtained from ray tomography and models obtained with FWI using ultrasound data.
Ultrasound computed tomography (USCT) is a promising imaging modality for breast cancer screening. Two challenges commonly arising in time-of-flight USCT are (1) to efficiently deal with large data sets and (2) to effectively mitigate the ill-posedness for an adequate reconstruction of the model. In this contribution, we develop an optimization strategy based on a stochastic descent method that adaptively subsamples the data, and analyze its performance in combination with different sparsity-enforcing regularization techniques. The algorithms are tested on numerical as well as real data obtained from synthetic phantom scans of the previous USCT Data Challenges.
We present a novel approach to obtain time-of-flight measurements between transducer pairs in an Ultrasound computed tomography (USCT) scanner by applying the interferometry principle, which has been used success- fully in seismic imaging to recover the subsurface velocity structure from ambient noise recordings. To apply this approach to a USCT aperture, random wavefields are generated by activating the emitting transducers in a random sequence. By correlating the random signals recorded by the receiving transducers, we obtain an approximation of the Green’s functions between all receiver pairs, where one is acting as a virtual source. This eliminates specific source imprints, and thus avoids the need for reference measurements and calibration. The retrieved Green’s functions between any two measurement locations can then be used as new data to invert the sound speed map. On the basis of the cross-correlation travel times a ray-based time-of-flight tomography is developed and solved with an iterative least-squares method. As a proof of concept, the algorithm is tested on numerical breast phantoms in a synthetic 2D study.
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