  An efficient computational approach for imaging binary-type physical
properties suitable for various models in biomedical applications is developed
and validated. The proposed methodology includes gradient-based multiscale
optimization with multilevel control space reduction based on principal
component analysis, optimal switching between the fine and coarse scales, and
their effective re-parameterization. The reduced dimensional controls are used
interchangeably at both scales to accumulate the optimization progress and
mitigate side effects. Computational efficiency and superior quality of
obtained results are achieved through proper communication between solutions
obtained at the fine and coarse scales. Reduced size of control spaces supplied
with adjoint-based gradients facilitates the application of this algorithm to
models of high complexity and also to a broad range of problems in biomedical
sciences and outside. The performance of the complete computational framework
is tested with 2D inverse problems of cancer detection by electrical impedance
tomography (EIT) in applications to synthetic models and models based on real
breast cancer images. The results demonstrate the superior performance of the
new method and its high potential for minimizing possibilities for false
positive and false negative screening and improving the overall quality of the
EIT-based procedures in medical practice.
