We propose a new imaging algorithm capable of producing quantitative indicator functions for unknown and possibly highly oscillating media from multi-static far field measurements of scattered fields at a fixed frequency. The algorithm exploits the notion of modified transmission eigenvalues and their determination from measurements. We propose in particular the use of a new modified background obtained as the limit of a metamaterial background. It has the advantage of having a unique non zero eigenvalue, which is particularly suited for the proposed imaging procedure. We show the efficiency of this new algorithm on some two dimensional experiments and emphasise its superiority with respect to some classical approaches such as the linear sampling method.

中文翻译：

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高度异构介质的平均指标重建

我们提出了一种新的成像算法，能够通过固定频率下散射场的多静态远场测量为未知且可能高度振荡的介质产生定量指示函数。该算法利用了修改后的传输特征值的概念及其根据测量的确定。我们特别建议使用新的修改背景作为超材料背景的限制。它的优点是具有独特的非零特征值，特别适合所提出的成像过程。我们在一些二维实验中展示了这种新算法的效率，并强调了它相对于一些经典方法（例如线性采样方法）的优越性。