Wavelet Based Color Image Compression and Mathematical Analysis of Sign Entropy Coding

One of the advantages of the Discrete Wavelet Transform (DWT) compared to Fourier Transform (e.g. Discrete Cosine Transform DCT) is its ability to provide both spatial and frequency localization of image energy. However, WT coefficients, like DCT coefficients, are defined by magnitude as well as sign. While algorithms exist for the coding of wavelet coefficients magnitude, there are no efficient for coding their sign. In this paper, we propose a new method based on separate entropy coding of sign and magnitude of wavelet coefficients. The proposed method is applied to the standard color test images Lena, Peppers, and Mandrill. We have shown that sign information of wavelet coefficients as well for the luminance as for the chrominance, and the refinement information of the quantized wavelet coefficients may not be encoded by an estimated probability of 0.5. The proposed method is evaluated; the results obtained are compared to JPEG2000 and SPIHT codec. We have shown that the proposed method has significantly outperformed the JPEG2000 and SPIHT codec as well in terms of PSNR as in subjective quality. We have proved, by an original mathematical analysis of the entropy, that the proposed method uses a minimum bit allocation in the sign information coding.