1926 IEEE TRANSACTIONS ONINSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 6, DECEMBER 2006 A Microwave Tomographic Imaging Approach for Multibistatic Configuration: The Choice of the Frequency Step Raffaele Persico, Francesco Soldovieri, and Giovanni Leone, Member, IEEE Abstract—This paper deals with the application of a frequency- domain microwave-tomography-imaging algorithm to a multi- bistatic configuration in ground-penetrating-radar applications. First, the authors formulate the inverse problem as a linear one by exploiting the Born approximation. Then, the reconstruction capabilities of the solution algorithm are investigated, and an optimal frequency step to be adopted for the reconstruction is discussed and determined. Finally, inversion results are presented with synthetic data obtained from time-domain simulations and then Fourier transformed in frequency domain. Index Terms—Born approximation (BA), electromagnetic scat- tering inverse problems, ground penetrating radar, microwave tomography, radar imaging. I. I NTRODUCTION G ROUND-PENETRATING radar (GPR) is a customary diagnostic tool in many applications such as archaeology, policy inquiries, and civil engineering [1]. Processing of GPR data can benefit from solution algorithms able to face the underlying inverse-scattering problem [2]. In particular, we are concerned with the determination of the spatial map of the dielectric and/or conductive properties within a given region embedded in the soil starting from scattered- field data gathered at the air–soil interface. The overall main purpose is to detect, locate, and determine the extent of the buried objects. It is well known that such a problem is ill-posed and nonlin- ear. The ill-posedness entails that the solution can be searched only within a finite dimensional space, and due to the nonlinear- ity, attention has to be devoted to the problem of possible false solutions [3]. Moreover, to account for the nonlinearity leads to a computationally burdening inversion algorithm. These difficulties can be overcome by the adoption of a linear model based on the Born approximation (BA) [4]–[6]. In this way, the problem of the false solutions is avoided, the computa- tional burden is reduced, and the reconstruction capabilities of the adopted-solution algorithm can be analyzed with reference Manuscript received August 15, 2005; revised May 24, 2006. R. Persico and F. Soldovieri are with the Istituto per il Rilevamento Elettromagnetico dell’Ambiente, 80124 Napoli, Italy (e-mail: soldovieri.f@ irea.cnr.it). G. Leone is with the Università di Reggio Calabria, 89060 Reggio Calabria, Italy (e-mail: gioleone@ing.unirc.it). Color versions of Figs. 4–6 are available at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2006.884346 to the spatial variations of the unknown dielectric profiles that can be retrieved. In particular, the singular-value decomposition (SVD) [7] of the linearized operator represents a tool for obtaining a stable solution of the problem, and in addition, it permits the analysis of the spatial variability of the class of retrievable unknowns in dependence of the measurement configuration [8], [9]. In particular, as a simple figure of the quantity and quality of the achievable independent information about the unknown, we make use of the spectral content [8]–[10], which is related to the Fourier transform of the functions spanning the finite dimensional space within which the solution is approximated. In [8], the spectral content has been theoretically evaluated in a two-dimensional (2-D) half-space geometry for the single frequency multiview/multistatic measurement configuration, and the expected behavior has been compared with the result of SVD-based analysis when truncation of the observation domain and uncertainties in data are taken into account. In [9], three measurement configurations (single view/multistatic/ multifrequency, multibistatic/multifrequency, and multistatic/ multifrequency/multiview) have been compared, and the multi- bistatic/multifrequency representation has been pointed out as a good solution in terms of computational and measurement cost and accuracy of the results. In [10], the role of the radiation pattern of the antennas has been discussed with regard to the class of the retrievable profiles and to the inaccuracy in the knowledge of the field of the antennas. Now, in this paper, we consider in further detail the multi- bistatic (also referred to as “common offset”) multifrequency configuration [1], [9], [11], [12], which is of wide practical interest as encountered in most commercial GPR systems. For such a configuration, a linear-inversion algorithm under the BA is implemented. The reconstruction capabilities of the solution algorithm are analyzed first by referring to an ideal measure- ment configuration with an infinite observation domain and a lossless soil. This provides algebraic relationships between the spectrum of the unknown function and the spectrum of the scattered field, so to employ the diffraction-tomography results, where the spatial Fourier-transform relationship between the object function and the scattered-field data is exploited in order to develop and analyze the solution algorithms [5], [8]–[10], [13]–[15]. In particular, we will focus on the problem of determining a suitable frequency step that ensures nonredundancy in the data. The practical relevance of this problem is related both to the 0018-9456/$20.00 © 2006 IEEE