Image recognition with the discrete rectangular-wave transform

In a previous paper [ J. Opt. Soc. Am. A5, 5 ( 1988)] the discrete rectangular-wave transform (DRWT), which is obtained by replacing sines and cosines in the discrete Fourier transform (DFT) by the discrete rectangular-wave function, was found to be superior to the DFT as a feature extractor in recognition tasks in terms of of simplicity, cost of use, and quality of performance. Here the DFT and the DRWT are compared further theoretically and experimentally by using computer simulations with respect to their performance in separating classes and their robustness in the presence of noise. In discriminant analysis, within-class and between-class scatter matrices are used to formulate criteria of class separability. Features are chosen so that they give maximum between-class scatter and minimum within-class scatter. Based on this measure, the DRWT is shown to be superior to the DFT in feature extraction. In noise analysis, performance is discussed in terms of the signal-to-noise ratios of the chosen features in the DRWT and the DFT spectral domains when the input noise is Gaussian. The DRWT leads to higher signal-to-noise ratios than does the DFT.