Resolution Enhancement of Spatial Parametric Methods via Regularization

Abstract

The spatial spectral estimation problem has applications in a variety of fields, including radar, telecommunications, and biomedical engineering. Among the different approaches for estimating the spatial spectral pattern, there are several parametric methods, as the well-known multiple signal classification (MUSIC). Parametric methods like MUSIC are reduced to the problem of selecting an integer-valued parameter [so-called model order (MO)], which describes the number of signals impinging on the sensors array. Commonly, the best MO corresponds to the actual number of targets, nonetheless, relatively large model orders also retrieve good-fitted responses when the data generating mechanism is more complex than the models used to fit it. Most commonly employed MO selection (MOS) tools are based on information theoretic criteria [e.g., Akaike information criterion (AIC), minimum description length (MDL) and efficient detection criterion (EDC)]. Normally, the implementation of these tools involves the eigenvalues decomposition of the data covariance matrix. A major drawback of such parametric methods (together with certain MOS tool) is the drastic accuracy decrease in adverse scenarios, particularly, with low signal-tonoise ratio, since the separation of the signal and noise sub-spaces becomes more difficult to achieve. Consequently, with the aim of refining the responses attained by parametric techniques like MUSIC, this article suggests utilizing regularization as a postprocessing step. Furthermore, as an alternative, this work also explores the possibility of selecting a single relatively large MO (rather than using MOS tools) and enhancing via regularization, the solutions retrieved by the treated parametric methods. In order to demonstrate the capabilities of this novel strategy, synthetic aperture radar (SAR) tomography (TomoSAR) is considered as application.

Statistical Regularization for TomoSAR Imaging With Multiple Polarimetric Observations

“…Described in [12], MUSIC improves performance with the use of dedicated MO selection tools, such as those based on information theoretic criteria. In addition, WISE might be employed as prost-processing step to enhance MUSIC's resolution.…”

“…PolMUSIC achieves a finer resolution than PolCapon. Moreover, it is worth recalling that the use of specific MO selection tools [12] may increase the performance of PolMU-SIC. In addition, PolMUSIC can be combined with PolWISE to improve the resolution.…”

“…2) Being PolWISE an iterative technique, over/under regularization is prevented by terminating the procedure at an appropriate iteration. Specifically, the iterative approach is terminated after reaching a solution that maximizes the KL information function [11], [12] via minimizing AIC, BIC or EDC. The novel strategy is assessed through simulations and on fully polarimetric TomoSAR airborne data at L-band, acquired from an urban scenario.…”

“…Parametric methods include techniques like MUSIC (summarized in [12]), whereas non-parametric ones include techniques like MSF and Capon. These three approaches are the most common TomoSAR focusing techniques, widely used (among other reasons) because of its simple implementation.…”

Spaceborne Multi-Baseline Synthetic Aperture Radar (SAR) Imaging

“…Tomography, i.e., 3D imaging via the formation of an additional aperture in across-track, allows a direct volumetric analysis of media like forests or ice sheets. Various new tomographic imaging techniques have been proposed in recent years to better suppress ambiguous responses or to better deal with small image stacks [21], [22]. Future spaceborne missions, like e.g.…”