Log-Euclidean Kernel Sparse Representation on DR-Spectral SPD Matrices for Signal Detection

In this paper, we propose a novel signal detection method in the framework of matrix information geometry and apply it to target detection in complex clutter. The sample data is first assumed to be constructed as a high-dimensional spectral SPD matrix by extracting the SIFT feature from the spectrogram obtained by STFT procedure. In this case, a high-dimensional SPD manifold is naturally modeled, which yields rich information from signal data. To eliminate the redundancy while preserve the original structure of the data, we first employ the dimensionality reduction (DR) method on the high-dimensional SPD manifold, then through Log-Euclidean Kernel sparse representation for the DR-spectral SPD matrices lying on a lower-dimensional SPD manifold, we finally perform a binary classification (the absence or presence of the objective signal) on a discriminative Reproducing Kernel Hilbert Space with low computational complexity. Similar researches, for instance, directly identify the spectral line or peak in the spectrogram, however, provide a poor description for signal data, which results in unsatisfactory detection performance. Experimental results based on real sea clutter show great information for complex signal detection tasks from signal data analysis with matrix information geometry, which can be widely used in signal processing.