Abstract
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.
Highlights
Microwave imaging is an emerging technology that is beginning to see increased clinical use for a number of applications
There is a substantial property contrast between benign and malignant tissue [8,9,10]; for stroke diagnosis, there is a large contrast between blood and normal brain tissue [11]; for bone, there is a significant correlation between the dielectric properties and bone density [7]
The reconstruction algorithm was finite element based, such that computing the Jacobian meant performing numerous integrations over the various triangular elements and sub-elements within the imaging zone just to calculate a single value within the matrix
Summary
Microwave imaging is an emerging technology that is beginning to see increased clinical use for a number of applications These include breast cancer imaging [1,2,3,4], stroke diagnosis [5,6], bone imaging [7] and others. Microwave holography generally assumes that the broadcast signal and those transmitted through and reflected back from the target are spherical waves which can be decomposed into a superposition of plane waves through a Fourier transform [16] Each of these can be back propagated to the target and re-transformed into the spatial domain for target identification and characterization.
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