This paper presents bit-plane based statistical study for integer wavelet transforms commonly used in image compression. In each bit-plane, the coefficients were modeled as binary random variables. Experimental results indicate the probability of the significant coefficients (P1), in each bit-plane, monotonically increases from P1 ≈ 0 at the most significant bits (MSB) to P1≈ 0.5 at the least significant bits (LSB). Then, a parameterized model to predict P1 from the MSB to the LSB was proposed. Also, the correlation among the different bit-planes within the same coefficient was investigated. In addition, this study showed correlation of the significant coefficients in the same spatial orientation among different subbands. Finally, clustering within the each subband and across the different subband with the same spatial orientation was investigated. Our results show strong correlation of previously coded significant coefficients at higher levels and the significant coefficients in future passes at lower levels. The overall study of this paper is useful in understanding and enhancing existing wavelet-based image compression algorithms such as SPIHT and EBC.
This paper presents a lossless coding that is designed for 16-bit high-resolution x-ray images. The proposed algorithm uses non-linear histogram-based mapping that eliminates the gaps in the histogram before applying wavelet transform. The mapping is designed to reduce the magnitude of the wavelet coefficients, especially in the high frequency subbands. Reducing the magnitude of the coefficients in the high frequency subbands provides more compression as the high frequency subbands occupy most of the image area. This paper shows that the energy of all the subbands is being reduced after eliminating the gaps in the histogram, and hence the magnitudes of the coefficients are being reduced. To further exploit this property, the image is segmented into 64×64 blocks, and the gaps in the histograms of each block are independently eliminated, and then each block is independently coded using SPIHT. Since the mapping is non-linear, look-up tables are transmitted to the decoder as part of the overhead information. Experimental results show that the compression in bit per pixel (bpp) of the proposed algorithm does not only exceed wavelet-based SPHIT and JPEG 2000 but also it exceeds the state-of-the-art context-based JPEG-LS.