A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast...

Area of Science:

• Computational electromagnetics
• Medical imaging technology
• Biomedical engineering

Background:

• Microwave tomography for breast imaging faces computational challenges.
• The forward field computation is a critical bottleneck in iterative inverse problems.
• Efficient algorithms are needed for practical breast imaging systems.

Purpose of the Study:

• To introduce an efficient discrete dipole approximation (DDA) for 2D electric field calculations.
• To optimize the forward problem computation for microwave tomography.
• To enable faster and lower-cost breast imaging systems.

Main Methods:

• Derived a 2D DDA algorithm for microwave tomography.
• Formulated the problem for the conjugate orthogonal conjugate gradient (COCG) method.
• Optimized matrix-vector multiplication using block-Toeplitz matrices and circulant matrices with FFT.

Main Results:

• Demonstrated accurate and efficient electric field calculations.
• Achieved significant computational speedup using the COCG-FFT approach.
• Compared performance against direct solvers and COCG.

Conclusions:

• The developed DDA formulation is accurate and efficient for microwave tomography.
• The COCG-FFT method offers substantial computational advantages.
• This approach is a key step towards developing low-cost, fast breast imaging for underserved populations.