A Gradient Descent Strategy for Improved Synthetic Discriminant Function Fringe-Adjusted Joint Transform Correlation

The SDF-FAJTC algorithm is a rotation- and shift-invariant correlation filter that can enable effective detection and localization of targets in Automatic Target Recognition (ATR) applications. However, the existing method for generating the key synthetic discriminant function (SDF) component of the SDF-FAJTC is an ad-hoc procedure that lacks solid mathematical foundation and is not guaranteed to converge. In this paper, we utilize the Gradient Descent concept to develop a more principled procedure for synthesizing the SDF filter. The SDF filter design problem is formulated as a mean-squared-error minimization that is solved using Gradient Descent. For gains in computational speed, the computation of the mean-squared-error is carried out in the frequency domain. Training and testing images were constructed using target chips from the Moving and Stationary Target Acquisition and Recognition (MSTAR) benchmarking datasets. Our promising results indicate that, compared to the existing implementation, our proposed implementation is more computationally-efficient and exhibits significantly higher Peak-to-Sidelobe Ratio (PSR) higher values which translates to higher accuracy for detecting and/or localizing targets within scenes of interest.