Wavelet array decomposition of images using a Hermite sieve

Abstract. Generalized Hermite polynomials are used in a novel way to arrive at a multi-layered representation of images. This representation, which is centred on the creation of a new class of wavelet arrays, is (i) distinct from what we find in the current literature, (ii) stable, and (iii) in the manner of standard transforms, transforms the image, explicitly, into matrices of coefficients, reminiscent of Fourier series, but at various scales, controlled by a scale parameter. Among the other properties of the wavelet arrays, (a) the shape of the resolution cell in the 'phase-space ' is variable even at a specified scale, depending on the nature of the signal under consideration; and (b) a systematic procedure is given for extracting the zero-crossings from the coefficients at various scales. This representation has been successfully applied to both synthetic and natural images, including textures