Wavelet array decomposition of images using a Hermite sieve

Generalized Hermite polynomials are used in a novel way to arrive at a multi-layered representation of images centred on the creation of a new class of wavelet arrays. 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 a systematic procedure is given for extracting the zero-crossings from the coefficients at various scales. This representation has been applied successfully to both synthetic and natural images, including texture