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.
Quadratic Correlation Filters have recently been used for Automatic Target Recognition (ATR). Among these, the Rayleigh Quotient Quadratic Correlation Filter (RQQCF) was found to give excellent performance when tested extensively with Infrared imagery. In the RQQCF method, the filter coefficients are obtained, from a set of training images, such that the response to the filter is large when the input is a target and small when the input is clutter. The method explicitly maximizes a class separation metric to obtain optimal performance. In this paper, a novel transform domain approach is presented for ATR using the RQQCF. The proposed approach, called the Transform Domain RQQCF (TDRQQCF) considerably reduces the computational complexity and storage requirements, by compressing the target and clutter data used in designing the QCF. Since the dimensionality of the data points is reduced, this method also overcomes the common problem of dealing with low rank matrices arising from the lack of large training sets in practice. This is achieved while retaining the high recognition accuracy of the original RQQCF technique. The proposed method is tested using IR imagery, and sample results are presented which confirm its excellent properties.
The Modified Eigenvalue problem arises in many applications such as Array Processing, Automatic Target Recognition (ATR), etc. These applications usually involve the Eigenvalue Decomposition (EVD) of matrices that are time varying. It is desirable to have methods that eliminate the need to perform an EVD every time the matrix changes but instead update the EVD adaptively, starting from the initial EVD. In this paper, we propose a novel Optimal Adaptive Algorithm for the Modified EVD problem (OAMEVD). Sample results are presented for an ATR application, which uses Rayleigh Quotient Quadratic Correlation filters (RQQCF). Using a Infrared (IR) dataset, the effectiveness of this new technique as well as its advantages are illustrated.
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