3d Microwave Tomography With Huber Regularization Applied to Realistic Numerical Breast Phantoms

Abstract

Abstract-Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2 GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration.

Microwave Breast Imaging With Prior Ultrasound Information

“…To improve the quality of the reconstruction and incorporate high frequency components of the image, one introduces prior information. Inspired by [8], [21], one incorporates Huber regularization into CSI.…”

“…However, less detailed information about the breast is made available [7]. To achieve a possibly better retrieval of the distribution of EM parameters within the breast, tomographic microwave imaging is widely used, refer to [8]- [10] among many others. In this approach, several transmitting and receiving antennas are set around the breast.…”

“…Two-fold SOM (TSOM) confines the reconstruction within a low-dimension subspace. Huber regularization [8], [21] and weighted L2norm total variation (TV) [22] smoothen small-scale noise while trying to preserve discontinuities. For piecewise constant profiles, value picking (VP) [23] regularization can be applied.…”

A Method for Effective Permittivity and Conductivity Mapping of Biological Scenarios via Segmented Contrast Source Inversion

“…Moreover, the measured data are affected by phase uncertainties [15]. As an alternative, microwave tomography (MWT) [16][17][18][19][20] could be exploited, as this technique indeed provides a low-cost and non-invasive modality to image the inside of the human body at the frequencies of interest for the above-mentioned applications. On the other hand, it is well known that, as compared to MRI and CT, MWT exhibits a low spatial resolution, which would ultimately impair the pursued goal (i.e., high resolution mapping of the EPs to build reliable computational models).…”

Embedding Approach to Modeling Electromagnetic Fields in a Complex Two-Dimensional Environment

“…For multidimensional problems, this requires a number of field computations for a varying physical parameter such as frequency or source position. The cost function then refers to the known measured field information and preferably includes a regularizing function of the configuration parameters [7][8][9]. In the so-called modified gradient method and subsequent generalizations, the configuration and the unknown fields are determined simultaneously [10,11].…”