Angela Dell'Aversano

SAR Imaging Algorithms and Some Unconventional Applications: A unified mathematical overview

This article deals with two significant aspects related to synthetic aperture radar imaging (SAR-I) of relevant theoretical and applicative interest. The first objective regards the analysis of the most-used SAR-I approaches under the unified mathematical framework provided by the Porter-Bojarski integral equation. The second objective is to provide an updated overview on how SAR-I research is generalizing previous algorithms to deal with unconventional scenarios.

Ground Clutter Removal in GPR Surveys

In GPR prospecting, strong reflections due to the background material interface can hinder the detection of localized buried scatterers, especially when the targets are close (in terms of probing wavelength) to the interface. Moreover, signals due to objects located outside the investigated domain and occurring in the observation time window may dramatically affect the reliability of the results. In order to mitigate such kind of clutter, an entropy based approach has been recently proposed in the frame of intra-wall diagnostic. In this paper, we assess the performance of such an approach by processing experimental data collected in laboratory controlled conditions and referred for the challenging situation of shallower dielectric and metallic targets, whose back-scattered fields overlap in time with the air-soil interface signal. In addition, a performance comparison of the proposed method is performed with other two approaches, i.e., the mean subtraction method and the subspace projection procedure.

INTERFEROMETRIC TIME REVERSAL MUSIC FOR SMALL SCATTERER LOCALIZATION

The problem of localizing small scatterers (in terms of wavelength) by Time Reversal-MUSIC (TR-MUSIC) algorithm is addressed. In particular, we focus on uniqueness problems that might arise for certain far zone conflgurations when noise corrupts data. These lead to reconstructions afiected by ghost targets from which it is di-cult to discern actual targets. In order to remedy such a drawback, data obtained at multiple frequencies are employed. In detail, a new multi-frequency version of TR-MUSIC is introduced. It consists in mixing reconstructions obtained at difierent frequencies. Numerical analysis shows that this method outperforms classical TR- MUSIC as well as its multi-frequency implementation already present in literature.

Some Remarks on Time-Reversal MUSIC for Two-Dimensional Thin PEC Scatterers

Time-reversal MUSIC is a super-resolving imaging method that allows localizing point-like scatterers with a resolution much smaller than the diffraction limits. In this letter, we check this statement for a populated scattering scene for the case of 2-D cylindrical perfect electric conducting objects. It is shown that when the data are corrupted even by a small amount of noise, there is an intrinsic limit on the number of scatterers that can be successfully detected. This number turns out to be linked with the so-called number of degrees of freedom corresponding to the spatial region where the targets are located. Moreover, it is shown that the transverse electric polarization is more sensitive to the noise as, given the size of the spatial region occupied by the scatterers, the maximum number of scatterers that can be detected is three times lower than that detectable by the transverse magnetic illumination.

A two step linear inversion strategy for imaging simple shapes

In this paper an innovative procedure for the localization and reconstruction of objects composed of elementary shapes is described. Sparse backscattered multifrequency field data are assumed to be known. The strategy is based on two steps in order to decrease the computational costs and to allow the use of few measurement points (with respect of Number of Degrees of Freedom). At first an Interferometric-Migration (IM) strategy is introduced with the purpose of reducing the dimension of the solution space. The second step is founded on the assumption that the elementary shapes are known and their geometrical features can characterized by a small amount of parameters. Then an Interferometric-MUSIC (I-MUSIC) algorithm is applied by combining results at single frequency. The overall approach is numerically tested in a 2D geometry for electrically large objects and has been proved robust against uncertainties on data.

Through the Wall Breathing Detection by Means of a Doppler Radar and MUSIC Algorithm

The problem of detecting the respiration rate of a human being located behind a wall is addressed using a continuous wave Radar. A Toeplitz based MUSIC algorithm is employed to detect the Doppler modulation induced by chest movements. This method, unlike other smoothing procedures, allows us to restore the rank of the correlation matrix without sacrificing the length of observation time interval and hence the resolution. Experimental results show that the proposed method outperforms the commonly used FFT procedure.

A combined approach for shape reconstruction from under-sampled data

A combined Migration-MUSIC approach is adopted to deal with the inverse problem of reconstructing the shape of strong scatterers composed of elementary shapes and embedded within an electrically large investigation domain from under-sampled backscattered field data. The scatterers are deployed over a metallic plane, which mimics the ground floor, as in SAR scenarios. In order to mitigate aliasing, migration images obtained by using disjoint available frequency bands are combined in an interferometric way. Next as each elementary shape is characterized by a small amount of parameters, a MUSIC algorithm is employed to reconstruct them separately.

A Strategy for Reconstructing Simple Shapes From Undersampled Backscattered Data

The shape reconstruction of a strong large scattering object made up of elementary shapes and embedded within a large investigation domain is dealt with from the undersampled multifrequency backscattered field data. First, a migration algorithm is run that, despite aliasing, allows reducing the spatial region, where the scatterer can be located. Then, the overall shape is determined by identifying the elementary ones through a multiple signal classification algorithm. The approach is numerically tested for a 2-D geometry, and it proves to be robust against uncertainties on data.

Comparing TM and TE music for point-like scatterers' localization

In this paper we examine Time Reversal MUSIC (TRM) performance for two orthogonal polarizations: TMz and TEz. It is shown that if a little amount of noise corrupts the data there is an intrinsic limit on the number of scatterers that can be successfully detected. This number turns out to be the so-called number of degrees of freedom of the scattered field. Moreover, it is found that Time Reversal MUSIC performance changes depending on the considered polarization.