  An efficient computational approach for optimal reconstructing parameters of
binary-type physical properties for models in biomedical applications is
developed and validated. The methodology includes gradient-based multiscale
optimization with multilevel control space reduction by using principal
component analysis (PCA) coupled with dynamical control space upscaling. The
reduced dimensional controls are used interchangeably at fine and coarse scales
to accumulate the optimization progress and mitigate side effects at both
scales. Flexibility is achieved through the proposed procedure for calibrating
certain parameters to enhance the performance of the optimization algorithm.
Reduced size of control spaces supplied with adjoint-based gradients obtained
at both scales facilitate the application of this algorithm to models of higher
complexity and also to a broad range of problems in biomedical sciences. This
technique is shown to outperform regular gradient-based methods applied to fine
scale only in terms of both qualities of binary images and computing time.
Performance of the complete computational framework is tested in applications
to 2D inverse problems of cancer detection by the electrical impedance
tomography (EIT). The results demonstrate the efficient performance of the new
method and its high potential for minimizing possibilities for false positive
screening and improving the overall quality of the EIT-based procedures.
