Statistical Distributions of Discrete Walsh Hadamard Transform Coefficients of Natural Images

For low bit rate applications, the discrete Walsh Hadamard transform (WHT) shows almost comparable results when compared to the popular discrete Cosine transform (DCT) in terms of compression efficiency, peak signal to noise ratio (PSNR) and visual results. The discrete WHT is a best choice which compromises between the computational complexity and compression efficiency. The great advantage of the discrete WHT is its relatively very low computational complexity when compared to DCT. However there is no definitive study reported in literature regarding the statistical distributions of discrete WHT coefficients of natural images. This study performs a2χ goodness of fit test to determine the distribution that best fits the discrete WHT coefficients. The simulation results show that the distribution of a majority of the significant AC coefficients can be modelled by the Generalized Gaussian distribution. The knowledge of the appropriate distribution helps in design of optimal quantizers that may lead to minimum distortion andhence achieve optimal coding efficiency.