A Numerical Study on the Sensitivity of Time-Reversal Imaging Methods Against Clutter, Noise and Model Perturbations

Time-reversal (TR) techniques using acoustical waves have shown to provide promising results for the detection and localization of scatterers in multiple scattering environments by providing super-resolution and statistical stability. These techniques exploit the TR invariance of the wave equation in lossless and stationary media, and involve the retransmission of scattering signals acquired by a set of receivers in a timereversed fashion. Back-propagated TR signals tend to focus around the original scatter location(s). Many TR applications require the analysis of the TR operator (TRO) obtained from the multistatic data matrix (MDM) of a TR array (TRA). In particular, the eigenvalue decomposition (EVD) of the TRO forms the basis for both the so-called DORT (decomposition of the TRO) and TR-MUSIC (TR multiple signal classification)4 methods. These two approaches are examples of TR imaging algorithms that rely on the use of complementary subspaces of the TRO. Specifically, DORT exploits the signal subspace (SS), whereas TR-MUSIC employs the null subspace (NS). For well-resolved point-like scatterers, location and strength information of the scatterers are associated with eigenvalues and respective eigenvectors of the SS of the TRO in a one-to-one fashion2. Therefore, backpropagation of these eigenvectors yields images of the primary targets. This constitutes the basis for TR imaging via DORT. On the other hand, regardless of well-resolvedness criteria, the NS space of the TRO is orthogonal to SS, i.e. the projection of any vector formed by the linear combination of SS eigenvectors onto the NS should (ideally) be zero. This is the basis of TR-MUSIC imaging. In this work, we investigate the performance of both DORT and TR-MUSIC against perturbations produced by clutter, model mismatch, and TR invariance breaking (due to losses in the background media), in both narrowband (NB) and ultrawideband (UWB) cases. We focus on frequency bands and sensor deployment scenarios typical of subsurface sensing problems. Clutter is produced from subsurface inhomogeneities modeled by continuous random media models based on soil parameters having spatially fluctuating Gaussian random permittivities and prescribed (also Gaussian) correlation functions. Perfectly conducting objects (PEC) embedded in the random media are considered as primary scatterers.