  An efficient computational approach for optimal reconstruction of binary-type
images suitable for models in various applications including biomedical imaging
is developed and validated. The methodology includes derivative-free
optimization supported by a set of sample solutions with customized geometry
generated synthetically. The reduced dimensional control space is organized
based on contributions from individual samples and the efficient
parameterization obtained from the description of the samples' geometry. The
entire framework has an easy-to-follow design due to a nominal number of tuning
parameters which makes the approach simple for practical implementation in
various settings, as well as for adjusting it to new models and enhancing the
performance. High efficiency in computational time is achieved through applying
the coordinate descent method to work with individual controls in the
predefined custom order. This technique is shown to outperform commonly used
gradient-based and other derivative-free methods with applied PCA-based control
space reduction in terms of both qualities of binary images and stability of
obtained solutions when noise is present in the measurement data. The
performance of the complete computational framework is tested in applications
to 2D inverse problems of detecting inclusions or defective regions by the
electrical impedance tomography (EIT). The results demonstrate the efficient
performance of the new method and its high potential for improving the overall
quality of the EIT-based procedures including biomedical applications.
