Ghent Univeristy

Funing.Bai@telin,ugent.be

Microwave Tomography in 2D and 3D piecewise constant targets

Simulated data: 2D objects from Frensel database

A homogeneous cylinder is embedded in a second homogeneous cylinder. The inner cylinder has a radius r_a= 15.5mm ≈ 0.2λ₀ (f=4GHz) and relative permittivity ε _r;a = 3. The outer cylinder has r_b = 40mm ≈ 0.5λ₀ and ε_r;b =1.45. The distance d between the centers of both cylinders is d = 5 mm.

Click the image to see the sparse configuration for 2D

Images in the same scale

Original	MS
SRVP	Proposed

Real data: 2D objects from Frensel database

Images in the same scale

Original	MS	SRVP	gs	Huber
Original	MS	SRVP	gs	Huber
Original	MS	SRVP	gs	Huber

Original FoamDielInt, FomaDielExt and TwinDiel images, and three results with MS, SRVP and Proposed methods.

Simulated data: 3D Objects

All targets measured in the 3D are guaranteed to lie in a 0.1 x 0.1 x 0.1 m³ cube. This cube is chosen as the reconstruction domain in the inverse solver and is discretized in 20 x 20 x 20 cube inverse problem voxels, yielding a total of 16000 permittivity unknowns.

Click the image to see the sparse configuration for 3D

A sphere

A homogeneous sphere with radius r_a = 30mm ≈ 0.8λ₀ and relative permittivity ε_r;a = 2 is positioned in the center of the antenna circle.

Images in the same scale

Original	MS
SRVP	Proposed

A cube in a sphere

The Object 2 is a cube with side 22.5mm and permittivity 2.5-1j, which is embedded in a sphere with radius 30mm and permittivity 1.8. The sphere and cube are centered at the origin and at the point (-5.6mm,-5.6mm,-5.6mm), respectively.

Images in the same scale

Original	MS
SRVP	Proposed

Top left: original. Top right: MS. Botoom left SRVP. Botoom right: the proposed method.

Real data: 3D Objects from Frensel database

Images in the same scale

Huber	TV-like	WCDA
Huber	TV-like	WCDA

Reconstructions of Two Spheres at 4GHz and a 3D view of the surface.

Related publications:

• Funing Bai, Aleksandra Pižurica, Wilfried Philips and Ann Franchois, "WCDA Regularization for 3D Quantitative Microwave Tomography", Inverse Problems, 2014

• Funing Bai, Aleksandra Pižurica, Bart Truyen, Ann Franchois, Sam Vanloocke, Daniël De Zutter and Wilfried Philips, "Weakly convex discontinuity adaptive regularization for microwave imaging", IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2013

• Funing Bai and Aleksandra Pižurica, "3D quantitative microwave imaging from sparsely measured data with Huber regularization", Paper 9020-13 Session 3: Modeling and Analysis of Multidimensional Data Computational Imaging XII, Electronic Imaging 2014, San Francisco, California, USA 2 - 6 February 2014 (SPIE2014).

• Funing Bai, Aleksandra Pižurica, Ann Franchois, and Wilfried Philips, "New insights in huber and TV-like regularizers in microwave imaging", International Conference on Image Processing (ICIP2013).

• Funing Bai, Aleksandra Pižurica, Sam Vanloocke, Ann Franchois, Daniël De Zutter and Wilfried Philips, "Quantitative microwave tomography from sparse measurements using a robust huber regularizer", International Conference on Image Processing (ICIP2012).