A 3-D Level Set Method for Microwave Breast Imaging

Objective: Conventional inverse-scattering algorithms for microwave breast imaging result in moderate resolution images with blurred boundaries between tissues. Recent 2-D numerical microwave imaging studies demonstrate that the use of a level set method preserves dielectric boundaries, resulting in a more accurate, higher resolution reconstruction of the dielectric properties distribution. Previously proposed level set algorithms are computationally expensive, and thus, impractical in 3-D. In this paper, we present a computationally tractable 3-D microwave imaging algorithm based on level sets. Methods: We reduce the computational cost of the level set method using a Jacobian matrix, rather than an adjoint method, to calculate Frechet derivatives. We demonstrate the feasibility of 3-D imaging using simulated array measurements from 3-D numerical breast phantoms. We evaluate performance by comparing full 3-D reconstructions to those from a conventional microwave imaging technique. We also quantitatively assess the efficacy of our algorithm in evaluating breast density. Results: Our reconstructions of 3-D numerical breast phantoms improve upon those of a conventional microwave imaging technique. The density estimates from our level set algorithm are more accurate than those of the conventional microwave imaging, and the accuracy is greater than that reported for mammographic density estimation. Conclusion: Our level set method leads to a feasible level of computational complexity for full 3-D imaging, and reconstructs the heterogeneous dielectric properties distribution of the breast more accurately than conventional microwave imaging methods. Significance: 3-D microwave breast imaging using a level set method is a promising low-cost, nonionizing alternative to current breast imaging techniques.