1594 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 8, AUGUST 2006 Reconstruction Quality and Spectral Content of an Electromagnetic Time-Domain Inversion Algorithm Andreas Fhager*, Parham Hashemzadeh, Student Member, IEEE, and Mikael Persson Abstract—A tomographic time-domain reconstruction algo- rithm for solving the inverse electromagnetic problem is described. The application we have in mind is dielectric breast cancer detec- tion but the results are of general interest to the field of microwave tomography. Reconstructions have been made from experimental and numerically simulated data for objects of different sizes in order to investigate the relation between the spectral content of the illuminating pulse and the quality of the reconstructed image. We have found that the spectral content is crucial for a successful reconstruction. The work has further shown that when imaging objects with different scale lengths it is an advantage to use a multiple step procedure. Low frequency content in the pulse is used to image the large structures and the reconstruction process then proceed by using higher frequency data to resolve small scale lengths. Good agreement between the results obtained from experimental data and simulated data has been achieved. Index Terms—FDTD methods, microwave imaging, microwave measurements, transient analysis. I. INTRODUCTION I N the late 1960s microwave transmission measurements as a technique to detect breast cancer tumors was suggested by Mallard and Lawn, [1], and Mallard and Whittingham, [2]. Their suggestion was based on measurements in the microwave region by England and Sharples, [3], and England, [4], who found that the permittivity of cancerous breast tissue is higher than for nonmalignant tumor and normal breast tissue. Later, several others groups have confirmed these findings, [5]–[8]. Breast cancer, which is the second common cancer form after lung cancer and the most common cancer form among women, [9], is today often detected using X-ray mammography, [10], [11]. Despite its wide usage there are a few problems related to this method. The most important is that 5%–15% of the tumors can not be seen mammographically, [11], [12]. Alternative or complementing imaging method are, therefore, needed. Tomographic microwave imaging is not limited to breast cancer imaging but the technique can be used in many different fields and applications. Some examples are subsurface sensing Manuscript received September 20, 2005; revised February 19, 2006. This work was supported in part by the Swedish Research Council, in part by the Knut and Alice Wallenberg Foundation, and in part by the National Graduate School in Scientific Computing, Sweden. Asterisk indicates corresponding author. *A. Fhager is with Chalmers University of Technology, Department of Signal and Systems, SE-412 96 Göteborg, Sweden (e-mail: andreas.fhager@chalmers. se). P. Hashemzadeh and M. Persson are with Chalmers University of Tech- nology, Department of Signal and Systems, SE-412 96 Göteborg, Sweden (e-mail: parham@chalmers.se; mikael.persson@chalmers.se). Digital Object Identifier 10.1109/TBME.2006.878079 such as geoscience, [13], and landmine detection. Other poten- tial applications are nondestructive testing of materials, [14] and different biomedical imaging, [15]. In active microwave imaging techniques, electromagnetic ra- diation is used to illuminate the object under test and the mea- sured scattered radiation is used to image the internal dielec- tric properties. Two principally different approaches are taken in order to detect the dielectric contrasts within the object, radar- like backscattering methods and tomographic methods. In the radar-like methods, an ultra-wideband signal is illuminating the object from several directions. The amplitude and the arrival time of the reflected signals are used to identify the position of the scatterers. No quantitative measures of the dielectric profile of the scattering targets are obtained but one rather attempts to identify strong scatterers, i.e., the tumors, from their scattering signature, [16]–[19]. In the case of tomographic imaging methods, one uses the measured scattering data to produce quantitative images of the dielectric profile. In the early days of microwave tomography research, different kind of computationally efficient linear approximations, primarily the Born and the Rytov approxima- tions, were used in the image reconstruction process, [20]–[24]. On electrically small objects with a low-contrast in the dielec- tric profile, these methods were found to be effective. However, when investigating larger objects with a higher contrast, such as biological tissue, these methods often fail, [25], [26]. Instead iterative nonlinear methods have to be used which usually involve defining a cost function that is either minimized or maximized, [27]. Since these algorithms are more computa- tionally demanding most of the research has been focused on two-dimensional (2-D) methods, where cross sectional slices of the object are imaged, using monochromatic radiation as the illuminating field, [28]–[33]. Extending the algorithms to three-dimensional (3-D) imaging is usually straight forward but increases the need for computational resources significantly. Some examples of recent work in 3-D have been reported, [34]–[40], and it is expected that large efforts will be made here in the future. To increase the resolution in the reconstructed image the fre- quency of the illuminating field is increased. While this leads to the possibility to resolve finer structures it also causes prob- lems when imaging large structures and high-contrast objects. The reason is that the scattered data is nonlinearly related to the scattering objects, and the nonlinearity is more pronounced for higher frequencies, [41]. As a result the algorithm often gets trapped in local minima, [42]. It is possible to overcome these difficulties by using a priori information about the object, [31], or by using multifrequency algorithms, such as the fre- quency-hopping approach, [43]. With the latter technique lower 0018-9294/$20.00 © 2006 IEEE