On the utilization of the adjoint method in microwave tomography

Area of Science:

• Electromagnetics and Imaging Science
• Computational Physics

Background:

• The adjoint method is vital for efficient model parameter updates in microwave imaging.
• Formulations vary significantly with imaging scenarios and optimization algorithms, potentially leading to overlooked differences.

Purpose of the Study:

• To classify adjoint method formulations into direct and indirect categories.
• To present, compare, and discuss these direct and indirect adjoint methods.
• To highlight the significance of appropriate adjoint method selection for computational efficiency.

Main Methods:

• Derivation of adjoint method formulations using the two-dimensional wave equation in frequency and time domains.
• Classification into direct (cost function derivative) and indirect (predicted data derivative) methods.
• Finite-difference time-domain simulations for single source-multiple receiver and multiple transceiver scenarios.

Main Results:

• Explicit derivations of direct and indirect adjoint methods are provided.
• Simulations demonstrate distinct applications of both methods across different microwave imaging configurations.
• The study confirms the impact of adjoint method choice on computational performance.

Conclusions:

• The direct and indirect adjoint methods offer distinct approaches to calculating update directions in microwave imaging.
• Understanding and selecting the correct adjoint method is critical for enhancing computational efficiency in optimization algorithms.
• This classification aids researchers in choosing the most suitable adjoint formulation for their specific microwave imaging problems.