Expansion of the nodal-adjoint method for simple and efficient computation of the 2d tomographic imaging jacobian matrix
Introductory text in journal, 2021

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

Computational efficiency

Microwave tomography

Jacobian matrix

Breast imaging

Nodal adjoint method

Discrete dipole approximation

Author

Samar Hosseinzadegan

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Biomedical Electromagnetics

Andreas Fhager

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Biomedical Electromagnetics

Mikael Persson

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering

Shireen D. Geimer

Thayer School of Engineering at Dartmouth

Paul M Meaney

Thayer School of Engineering at Dartmouth

Sensors

1424-8220 (ISSN) 1424-3210 (eISSN)

Vol. 21 3 1-16 729

Subject Categories

Computational Mathematics

Computer Science

Medical Image Processing

DOI

10.3390/s21030729

PubMed

33499014

More information

Latest update

2/11/2021