Convolve and Conquer: Data Comparison with Wiener Filters

Quantitative evaluations of differences and/or similarities between data samples define and shape optimisation problems associated with learning data distributions. Current methods to compare data often suffer from limitations in capturing such distributions or lack desirable mathematical properties for optimisation (e.g. smoothness, differentiability, or convexity). In this paper, we introduce a new method to measure (dis)similarities between paired samples inspired by Wiener-filter theory. The convolutional nature of Wiener filters allows us to comprehensively compare data samples in a globally correlated way. We validate our approach in four machine learning applications: data compression, medical imaging imputation, translated classification, and non-parametric generative modelling. Our results demonstrate increased resolution in reconstructed images with better perceptual quality and higher data fidelity, as well as robustness against translations, compared to conventional mean-squared-error analogue implementations.

Computationally efficient full-waveform inversion of the brain using frequency-adaptive grids and lossy compression

A tomographic technique called full-waveform inversion has recently shown promise as a fast, affordable, and safe modality to image the brain using ultrasound. However, its high computational cost and memory footprint currently limit its clinical applicability. Here, we address these challenges through a frequency-adaptive discretisation of the imaging domain and lossy compression techniques. Because full-waveform inversion relies on the adjoint-state method, every iteration involves solving the wave equation over a discretised spatiotemporal grid and storing the numerical solution to calculate gradient updates. The computational cost depends on the grid size, which is controlled by the maximum frequency being modelled. Since the propagated frequency typically varies during the reconstruction, we reduce reconstruction time and memory use by allowing the grid size to change throughout the inversion. Moreover, we combine this approach with multiple lossy compression techniques that exploit the sparsity of the wavefield to further reduce its memory footprint. We explore applying these techniques in the spatial, wavelet, and wave atom domains. Numerical experiments using a human-head model show that our methods lead to a 30% reduction in reconstruction time and up to three orders of magnitude less memory, while negligibly affecting the accuracy of the reconstructions.

Stride: a flexible platform for high-performance ultrasound computed tomography

Advanced ultrasound computed tomography techniques like full-waveform inversion are mathematically challenging and orders of magnitude more computationally expensive than conventional ultrasound imaging methods. This computational and algorithmic complexity, and a lack of open-source libraries in this field, represent a barrier preventing the generalised adoption of these techniques, slowing the pace of research and hindering reproducibility. Consequently, we have developed Stride, an open-source Python library for the solution of large-scale ultrasound tomography problems. On one hand, Stride provides high-level interfaces and tools for expressing the types of optimisation problems encountered in medical ultrasound tomography. On the other, these high-level abstractions seamlessly integrate with high-performance wave-equation solvers and with scalable parallelisation routines. The wave-equation solvers are generated automatically using Devito, a domain specific language, and the parallelisation routines are provided through the custom actor-based library Mosaic. Through a series of examples, we show how Stride can handle realistic tomographic problems, in 2D and 3D, providing intuitive and flexible interfaces that scale from a local multi-processing environment to a multi-node high-performance cluster.

Spatial response identification enables robust experimental ultrasound computed tomography

Ultrasound computed tomography techniques have the potential to provide clinicians with 3D, quantitative and high-resolution information of both soft and hard tissues such as the breast or the adult human brain. Their practical application requires accurate modelling of the acquisition setup: the spatial location, orientation, and impulse response of each ultrasound transducer. However, existing calibration methods fail to accurately characterise these transducers unless their size can be considered negligible when compared to the dominant wavelength, which reduces signal-to-noise ratios below usable levels in the presence of high-contrast tissues such as the skull. In this paper, we introduce a methodology that can simultaneously estimate the location, orientation, and impulse response of the ultrasound transducers in a single calibration. We do this by extending spatial response identification, an algorithm that we have recently proposed to estimate transducer impulse responses. Our proposed methodology replaces the transducers in the acquisition device with a surrogate model whose effective response matches the experimental data by fitting a numerical model of wave propagation. This results in a flexible and robust calibration procedure that can accurately predict the behaviour of the ultrasound acquisition device without ever having to know where the real transducers are or their individual impulse response. Experimental results using a ring acquisition system show that spatial response identification produces calibrations of significantly higher quality than standard methodologies across all transducers, both in transmission and in reception. Experimental full-waveform inversion reconstructions of a tissue-mimicking phantom demonstrate that spatial response identification generates more accurate reconstructions than those produced with standard calibration techniques.