Resolution Enhancement of Spatial Parametric Methods via Regularization

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, minimum description length and efficient detection criterion). 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-to-noise ratio, since the separation of the signal and noise subspaces 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 article 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 tomography is considered as application.