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In this work, we investigate a class of elliptic inverse problems and aim tosimultaneously recover multiple inhomogeneous inclusions arising from twodifferent physical parameters, using very limited boundary Cauchy datacollected only at one or two measurement events. We propose a new fast, stableand highly parallelable direct sampling method (DSM) for the simultaneousreconstruction process. Two groups of probing and index functions areconstructed, and their desired properties are analyzed. In order to identifyand decouple the multiple inhomogeneous inclusions of different physicalnature, we introduce a new concept of mutually almost orthogonality propertythat generalizes the important concept of almost orthogonality property inclassical DSMs for inhomogeneous inclusions of same physical nature. With thehelp of this new concept, we develop a reliable strategy to distinguish twodifferent types of inhomogeneous inclusions with noisy data collected at one ortwo measurement events. We further improve the decoupling effect by choosing anappropriate boundary influx. Numerical experiments are presented to illustratethe robustness and efficiency of the proposed method.

A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature