Partial-Aliasing Correlation Filters

Correlation filters (CFs) are useful tools for detecting and locating signals or objects within a larger signal or scene of interest. Typically, these filters are designed during the training stage without worrying about how the cross-correlation between a test signal and the designed CF template will be carried out during the testing or use stage. Because of its computational benefits, the Fast Fourier Transform (FFT) algorithm is usually used for performing cross-correlations, leading to circular correlations and aliasing in the resulting correlation outputs. The aliasing effects can be suppressed by zero-padding, but at the expense of using longer FFTs and thus incurring more computational complexity. In this paper, we present a new approach where CFs are designed to explicitly allow partial aliasing at test time (thus allowing the use of shorter FFTs). This approach of allowing aliasing in the cross-correlation output and explicitly taking such partial aliasing into account when designing the CF is diametrically opposite to the conventional CF approaches which try to avoid aliasing effects. We demonstrate through numerical results that these new partial-aliasing correlation filters (PACFs) achieve better recognition performance than conventional CFs when used in block filtering architectures that allow aliasing.