A performance comparison of the transform domain Rayleigh quotient quadratic correlation filter (TDRQQCF) approach to the regularized RQQCF

Abstract

The Rayleigh Quotient Quadratic Correlation Filter (RQQCF) has been used to achieve very good performance for Automatic Target Detection/Recognition. The filter coefficients are obtained as the solution that maximizes a class separation metric, thus resulting in optimal performance. Recently, a transform domain approach was presented for ATR using the RQQCF called the Transform Domain RQQCF (TDRQQCF). The TDRQQCF considerably reduced the computational complexity and storage requirements, by compressing the target and clutter data used in designing the QCF. In addition, the TDRQQCF approach was able to produce larger responses when the filter was correlated with target and clutter images. This was achieved while maintaining the excellent recognition accuracy of the original spatial domain RQQCF algorithm. The computation of the RQQCF and the TDRQQCF involve the inverse of the term A1 = Rx + Ry where Rx and Ry are the sample autocorrelation matrices for targets and clutter respectively. It can be conjectured that the TDRQQCF approach is equivalent to regularizing A1. A common regularization approach involves performing the Eigenvalue Decomposition (EVD) of A1, setting some small eigenvalues to zero, and then reconstructing A1, which is now expected to be better conditioned. In this paper, this regularization approach is investigated, and compared to the TDRQQCF.