Multitransform applications for representing 3-D spatial and spatio-temporal signals

A novel technique, for the representation of three-dimensional signals employing constrained sets of basis functions of two or more transforms, is presented. The signal is split into subsignals, each of which is represented by the dominant components of a transform, whose basis functions closely approximate the subsignal. The residual error, which is the difference between the original and the reconstructed signal is properly formulated. An adaptive algorithm is developed to minimize this error and to maximize the signal to noise ratio (SNR) of the reconstructed signal for a fixed number of transform components. Simulations are presented to represent spatio-temporal signals as well as 3-D spatial signals by superimposing subsets from the DCT and Walsh transforms. It is shown that the proposed technique yields superior results in comparison with the single transform approach. An efficient possible coding strategy is also proposed for the transform coefficients.