Imaging highly heterogeneous media using transmission eigenvalues

We propose an imaging algorithm capable of constructing a quantitative macroscopic indicators of a highly cluttered media from multi-static data at a fixed frequency, without relying on a direct solver nor any linearisation assumptions on the inverse problem. The algorithm principle is similar to the one introduced in [3] as it exploits the notion of transmission eigenvalues and the capabilities of identifying them from multi static data using the Generalised Linear Sampling Method [4]. The novelty in our work is the replacement of transmission eigenvalues by the ones associated with a carefully designed artificial background, allowing us to work at a fixed frequency. The structure of the spectral problem associated with modified background is chosen so that only one eigenvalue exists, which provides stability and efficiency in the construction of the indicator function. We numerically demonstrate how the obtained algorithm is capable of providing meaningful averaging values of the physical parameters in cluttered media.