Development and verification of an adaptive algorithm to efficiently represent three-dimensional signals using mixed transforms

A novel technique for representation of three-dimensional signals is presented employing the constrained set of basis functions of two or more transforms. 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. A simulation is presented to represent a synthetic 3-D signal consisting of three cosine waves and three square waves, employing the DCT-Walsh mixed transforms. It is verified that it is possible to split the signal spectrally into a narrowband and a broadband part, thus allowing the DCT to represent the cosine waves and the Walsh Hadamard transform to represent the square waves. This leads to excellent data compression