Performance of the Barzilai-Borwein fixed-step optimization approach in non-invasive microwave imaging

In this paper, the performance of the Barzilai-Borwein non-line search descent is investigated as an inversion strategy for solving the nonlinear inverse scattering problem of Ultra-Wide Band (UWB) microwave tomographic imaging. The appealing feature of reducing the computational time by avoiding extensive line search calculations is tested. The capability of this method in solving cases of high nonlinearity, due to dense and complicated tissue structures, is evaluated and compared to the classical steepest decent, and the conjugate gradient approaches. Cross-sectional slices of glandular human breast tissue structures derived from MRI numerical data phantoms are used and tested with the presence of cancerous tissue. Reconstructed images are presented and discussed with particular attention to the image reconstruction time, and the accuracy of the outcome. Results indicate that the Barzilai-Borwein fixed-step approach outperforms the others in terms of accuracy, overall convergence, and susceptibility to local minima traps, although requiring a greater number of iterations.