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) dist
inct from what we find in the current literature, (ii) stable, and (ii
i) in the manner of standard transforms, transforms the image, explici
tly, into matrices of coefficients, reminiscent of Fourier series, but
at various scales, controlled by a scale parameter. Among the other p
roperties 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 coeffici
ents at various scales. This representation has been successfully appl
ied to both synthetic and natural images, including textures.