Automatic production of quantisation matrices based on perceptual modelling of wavelet coefficients for grey scale images

Wavelet domain statistical models have been shown to be useful for certain applications, e.g. image compression, watermarking and Gaussian noise reduction. One of the main problems for wavelet-based compression is to overcome quantisation error efficiently. Inspired by Weber-Fechners Law, we introduce a logarithmic model that approximates the non-linearity of human perception and partially precompensates for the effect of the display device. A logarithmic transfer function is proposed in order to spread the coefficients distribution in the wavelet domain in compliance with the human perceptual attributes. The standard deviation σ of the logarithmically-scaled coefficients in a subband represents the average difference from the mean of the coefficients in that subband. The standard deviation is chosen as a measure of the visibility threshold within this subband. Computing the values of σ's for all subbands results in a quantisation matrix for a chosen image. The quantisation matrix is then scaled by a factor ρ in order to provide the best trade-off between the visual quality and the bit-rate of the processed image. A major advantage of this model is to allow for observing the visibility threshold and automatically produce the quantisation matrix that is content dependant and scalable without further interaction from the user. The experimental results have proven the model works for any wavelet.