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Inverse Scattering Problem and Microwave Mammography

  • Jan 1, 2023
  • Kenjiro Kimura +13 more
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Abstract

There had been two approaches for visualising the tissues within an area of interest in the body. One involves the steps of acquiring shadowgraphs using a highly transmissive electromagnetic field, which is widely used in technologies such as X-ray computed tomography and nuclear magnetic resonance, and then constructing three-dimensional (3D) images from multiple shadowgraphs using computational calculation. The other involves converging highly scatterable waves using a lens and connecting data reflected from convergent points to construct images. The former method requires penetrability with no degree of freedom in wave selection, whereas the latter method does not enable visualisation of the background behind the reflecting object, and consequently obtain only surficial images. In this context, we addressed the inverse scattering problem, which had remained unsolved in the history of applied mathematics field, aiming to develop a universal methodology that outperforms the above two principles for ‘viewing objects’. Our efforts have been fruitful, as we established a scattering field theory that made it possible to solve this problem analytically. This theory proposes that 3D images can be precisely constructed by mathematically converging any points inside an object using measured data of scattered waves. This paper introduces not only the significance of the scattering field theory and the measurement principles but also a wide variety of cases in which the breast cancer tissue in the breast was visualised three-dimensionally using microwaves.

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