The inverse problem of body's heterogeneity recovery for early diagnostics of diseases using microwave tomography

Background. The aim of this work is to theoretical and numerical study the inverse scalar problem of diffraction by a volume obstacle characterized by a piecewise Hoelder-continuous function. Material and methods. The original boundary value problem is considered in the quasiclassical formulation and then reduced to a system of weakly singular integral equations; the properties of the latter system are studied using the potential theory and Fourier transform. Results. The inverse problem of diffraction is given the integral formulation; the theorem on uniqueness of a piecewise constant solution to the integral equation of the first type is proved; a new two-step algorythm for numerical solving the inverse problem is proposed and implemented; several numerical tests have been carried out. Conclusions. The obtained theoretical and numerical results confirm high efficiency of the proposed method, which can be applied for solving problems of near-field tomography.