Microwave Imaging of Three-Dimensional Targets by Means of an Inexact-Newton-Based Inversion Algorithm

A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three-dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem. The ill-posedness of the problem is faced by the application of an inexact-Newton method. Preliminary reconstruction results are reported

An inverse scattering procedure in Lebesgue spaces with non-constant exponents

Within the ever-growing field of electromagnetic imaging, inversion procedures are conventionally described in the mathematical framework of Hilbert spaces. Usually, the over-smoothing effects and oscillations that arise using a Hilbert-space formulation make the dielectric reconstruction of targets inaccurate. This problem is strongly reduced by the recent development of inversion techniques in Banach spaces. However, the selection of the Banach space norm parameter is critical for obtaining precise reconstructions, and no exact rules exist for this choice. To overcome this issue, an innovative approach in variable exponent Lebesgue spaces is proposed here, along with a preliminary numerical validation

A conjugate gradient like method for p-norm minimization in functional spaces.

We develop an iterative algorithm to recover the minimum p-norm solution of the functional linear equation Ax=b, where A:X⟶Y is a continuous linear operator between the two Banach spaces X=Lp, 11, with x∈X and b∈Y. The algorithm is conceived within the same framework of the Landweber method for functional linear equations in Banach spaces proposed by Schöpfer et al. (Inverse Probl 22:311–329, 2006). Indeed, the algorithm is based on using, at the n-th iteration, a linear combination of the steepest current “descent functional” A∗J(b−Axn) and the previous descent functional, where J denotes a duality map of the Banach space Y. In this regard, the algorithm can be viewed as a generalization of the classical conjugate gradient method on the normal equations in Hilbert spaces. We demonstrate that the proposed iterative algorithm converges strongly to the minimum p-norm solution of the functional linear equation Ax=b and that it is also a regularization method, by applying the discrepancy principle as stopping rule. According to the geometrical properties of Lp spaces, numerical experiments show that the method is fast, robust in terms of both restoration accuracy and stability, promotes sparsity and reduces the over-smoothness in reconstructing edges and abrupt intensity changes

Microwave Imaging of 3D Dielectric Structures by Means of a Newton-CG Method in Spaces

An increasing number of practical applications of three-dimensional microwave imaging require accurate and efficient inversion techniques. In this context, a full-wave 3D inverse-scattering method, aimed at characterizing dielectric targets, is described in this paper. In particular, the inversion approach has a Newton-based structure, in which the internal linear solver is a conjugate gradient-like algorithm in lp spaces. The presented results, which include the inversion of both numerical and experimental scattered-field data obtained in the presence of homogeneous and inhomogeneous targets, validate the reconstruction capabilities of the proposed technique

A non-Hilbertian inversion technique for the diagnosis of faulty elements in antenna arrays

Nowadays, antenna arrays are important tools adopted in a great number of applications including radar, mobile and satellite communication systems, and electromagnetic imaging. Moreover, in these applications, arrays with a high number of elements are ever more requested, which results in a growing possibility of damages in the array. The identification of defective components in array of antennas is really significant due to their applicative use: indeed, faulty detected elements can be fixed, thus avoiding to replace the whole antenna. In this work, a diagnostic technique for planar antenna arrays is presented. This approach enables recovering the eventually defective elements of the antenna under test using far-field data. To this end, an inversion approach established outside the standard context of Hilbertian spaces is used to address an inverse-source problem. A numerical validation concerning simple array antennas has been carried out to study the performances of the approach versus some antenna parameters, e.g., the size of the array

Detection of failures in antenna arrays through a Lebesgue-space approach

In this paper, a novel antenna array diagnostic approach is presented. The failures in antenna arrays are detected by means of a non-Hilbertian Lebesgue-space L-p technique to solve the underlying inverse problem. The solution of this inverse problem enables to retrieve the distribution of faulty feed excitations of the antenna under test starting from far-field measurements. The developed approach has been numerically validated. Simulations concern planar arrays where different rates and distributions of failures have been tested. Results show good capabilities in detecting damaged regions in the analyzed scenarios

Microwave imaging of mixed metallic–dielectric configurations via a finite element-based variable exponent approach

The quantitative reconstruction of structures that include both metallic and dielectric targets at the same time is addressed in this article. In particular, a nonlinear tomographic inversion approach developed in variable exponent Lebesgue spaces with a finite element (FE) formulation is adopted for the first time in such a configuration. Results obtained within a simulated environment are presented to validate the proposed technique and analyze the effects of different numbers and sizes of the metallic targets present in the investigated scenario. Moreover, the impact of possible a priori knowledge of metallic structures is assessed

A Banach Space Regularization Approach for Multifrequency Microwave Imaging

A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain) is inverted by using an inexact-Newton method developed in L p Banach spaces. In particular, the extension of the approach to multifrequency data processing is reported. The mathematical formulation of the new method is described and the results of numerical simulations are reported and discussed, analyzing the behavior of the multifrequency processing technique combined with the Banach spaces reconstruction method

On the trade-off between enhancement of the spatial resolution and noise amplification in conical-scanning microwave radiometers

The ability to enhance the spatial resolution of measurements collected by a conical-scanning microwave radiometer (MWR) is discussed in terms of noise amplification and improvement of the spatial resolution. Simulated (and actual) brightness temperature profiles are analyzed at variance of different intrinsic spatial resolutions and adjacent beams overlapping modeling a simplified 1-D measurement configuration (MC). The actual measurements refer to Special Sensor Microwave Imager (SSM/I) data collected using the 19.35 and the 37.00 GHz channels that match the simulated configurations. The reconstruction of the brightness profile at enhanced spatial resolution is performed using an iterative gradient method which allows a fine tuning of the level of regularization. Objective metrics are introduced to quantify the enhancement of the spatial resolution and noise amplification. Numerical experiments, performed using the simplified 1-D MC, show that the regularized deconvolution results in negligible advantages when dealing with low-overlapping/fine-spatial-resolution configurations. Regularization is a mandatory step when addressing the high-overlapping/low-spatial-resolution case and the spatial resolution can be enhanced up to 2.34 with a noise amplification equal to 1.56. A more stringent requirement on the noise amplification (up to 0.6) results in an improvement of the spatial resolution up to 1.64.Peer ReviewedPostprint (author's final draft

An enhanced resolution brightness temperature product for future conical scanning microwave radiometers

An enhanced spatial resolution brightness temperature product is proposed for future conical scan microwave radiometers. The technique is developed for Copernicus Imaging Microwave Radiometer (CIMR) measurements that are simulated using the CIMR antenna pattern at the L-band and the measurement geometry proposed in the Phase A study led by Airbus. An inverse antenna pattern reconstruction method is proposed. Reconstructions are obtained using two CIMR configurations, namely, using measurements collected at L-band by the forward (FWD) scans only, and combining forward and backward (FWD+BWD) scans. Two spatial grids are adopted, namely, 3 km x 3 km and 36 km x 36 km. Simulation results, referred to synthetic and realistic reference brightness fields, demonstrate the soundness of the proposed scheme that provides brightness temperature fields reconstructed at a spatial resolution up to ~ 1.9 times finer than the measured field when using the FWD+BWD combination.The work of Claudio Estatico was supported in part by the Gruppo Nazionale di Calcolo Scientifico–Istituto Nazionale di Alta Matematica (GNCS-INDAM), Italy. This work has been produced for the European Space Agency (ESA) in the frame of the Copernicus Program as a partnership between ESA and the European Commission.Peer ReviewedPostprint (author's final draft