Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix

On the utilization of the adjoint method in microwave tomography

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Impact of Skin on Microwave Tomography in the Lossy Coupling Medium

In microwave imaging, the effects of skin on recovering property distributions of tissue underneath the surface may be significant because it has high dielectric contrast with subcutaneous fat, which inevitably causes significant signal reflections. While the thickness of skin, especially relative to the wavelengths in use, would presumably have minor effects, it can introduce practical difficulties, for instance, in reflection-based imaging techniques, where the impact of the skin is large-often as high as two orders of magnitude greater than that of signals from underlying tumors in the breast imaging setting. However, in tomography cases utilizing transmission-based measurement data and lossy coupling materials, the situation is considerably different. Accurately implementing a skin layer for numerical modeling purposes is challenging because of the need to discretize the size and shape of the skin without increasing computational overhead substantially. In this paper, we assess the effects of the skin on field solutions in a realistic 3D model of a human breast. We demonstrate that the small changes in transmission field values introduced by including the skin cause minor differences in reconstructed images.

Discrete Dipole Approximation-Based Microwave Tomography for Fast Breast Cancer Imaging

This paper describes a fast microwave tomography reconstruction algorithm based on the two-dimensional discrete dipole approximation. Synthetic data from a finite-element based solver and experimental data from a microwave imaging system are used to reconstruct images and to validate the algorithm. The microwave measurement system consists of 16 monopole antennas immersed in a tank filled with lossy coupling liquid and a vector network analyzer. The low-profile antennas and lossy nature of system make the discrete dipole approximation an ideal forward solver in the image reconstructions. The results show that the algorithm can readily reconstruct a 2D plane of a cylindrical phantom. The proposed forward solver combined with the nodal adjoint method for computing the Jacobian matrix enables the algorithm to reconstruct an image within 6 seconds. This implementation provides a significant time savings and reduced memory requirements and is a dramatic improvement over previous implementations.