13 March 2017 Optimal experimental design to position transducers in ultrasound breast imaging
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Abstract
We present methods to optimize the setup of a 3D ultrasound tomography scanner for breast cancer detection. This approach provides a systematic and quantitative tool to evaluate different designs and to optimize the con- figuration with respect to predefined design parameters. We consider both, time-of-flight inversion using straight rays and time-domain waveform inversion governed by the acoustic wave equation for imaging the sound speed. In order to compare different designs, we measure their quality by extracting properties from the Hessian operator of the time-of-flight or waveform differences defined in the inverse problem, i.e., the second derivatives with respect to the sound speed. Spatial uncertainties and resolution can be related to the eigenvalues of the Hessian, which provide a good indication of the information contained in the data that is acquired with a given design. However, the complete spectrum is often prohibitively expensive to compute, thus suitable approximations have to be developed and analyzed. We use the trace of the Hessian operator as design criterion, which is equivalent to the sum of all eigenvalues and requires less computational effort. In addition, we suggest to take advantage of the spatial symmetry to extrapolate the 3D experimental design from a set of 2D configurations. In order to maximize the quality criterion, we use a genetic algorithm to explore the space of possible design configurations. Numerical results show that the proposed strategies are capable of improving an initial configuration with uniformly distributed transducers, clustering them around regions with poor illumination and improving the ray coverage of the domain of interest.
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Naiara Korta Martiartu, Naiara Korta Martiartu, Christian Boehm, Christian Boehm, Nicolas Vinard, Nicolas Vinard, Ivana Jovanović Balic, Ivana Jovanović Balic, Andreas Fichtner, Andreas Fichtner, } "Optimal experimental design to position transducers in ultrasound breast imaging", Proc. SPIE 10139, Medical Imaging 2017: Ultrasonic Imaging and Tomography, 101390M (13 March 2017); doi: 10.1117/12.2252514; https://doi.org/10.1117/12.2252514
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