Adaptive transform coding of images using approximate trigonometric expansions

The objective behind transform coding is to transform a data array into a statistically uncorrelated set. The uneven distribution of energy in transform coefficients is exploited for compression purposes, with significant energies considered for further processing. Block transforms, particularly the discrete cosine transform, have been used in image-video coding. An approximate Fourier expansion (AFE) of non-periodic signals with theoretically uncorrelated coefficients has been previously proposed. Furthermore, the capabilities of an approximate cosine expansion (ACE) have been explored for purposes of image coding. In this paper, we apply an approximate trigonometric expansion to images and investigate the potential of adaptive coding using blocks of images. The variable length basis functions computed by varying a user-defined parameter of the expansion will be used for adaptive transform coding of images. For comparison purposes, the results are compared with discrete cosine transform (DCT). Computer simulation results will also be presented.