It is often desirable in image processing to represent image structure in terms of a set of coefficients on a family of expansion functions. For example, familiar approaches to image coding, feature extraction, image segmentation, statistical and spectral analysis, and compression, involve such methods. It has invariably been necessary that the expansion functions employed comprise an orthogonal basis for the image space, because the problem of obtaining the correct coefficients on a non-orthogonal set of expansion functions is usually arduous if not impossible. Oddly enough, image coding in biological visual systems clearly involves non-orthogonal expansion functions. The receptive field profiles of visual neu-rons with linear response properties have large overlaps and large inner products, and are suggestive of a conjoint (spatial and spectral) "2-D Gabor representation" (Daugman 1980, 1985). The 2-D Gabor transform has useful decorrelating properties and provides a conjoint image description resembling a speech spectrogram, in which local 2-D image regions are analyzed for orientation and spatial frequency content, but its expansion functions are non-orthogonal. This paper describes a three-layered relaxation "neural network" that efficiently computes the correct coefficients for this and other, non-orthogonal, image transforms. Examples of applications which are illustrated include: (1) image compression to below 1.0 bit/pixel, and (2) textural image segmentation based upon the statistics of the 2-D Gabor coefficients found by the relaxation network.