A two-layered wavelet-based algorithm for efficient lossless and lossy image compression

In this paper, we propose a wavelet-based image-coding scheme allowing lossless and lossy compression, simultaneously. Our two-layered approach utilizes the best of two worlds: it uses a highly performing wavelet-based or wavelet packet-based coding technique for lossy compression in the low bit range as a first stage. For the second (optional) stage, we extend the concept of reversible integer wavelet transforms to the more flexible class of adaptive reversible integer wavelet packet transforms which are based on the generation of a whole library of bases, from which the best representation for a given residue between the reconstructed lossy compressed image and the original image is chosen using a fast-search algorithm. We present experimental results demonstrating that our compression algorithm yields a rate-distortion performance similar or superior to the best currently published pure lossy still image-coding methods. At the same time, the lossless compression perf ormance of our two-layered scheme is comparable to that of state-of-the-art pure lossless image-coding schemes. Compared to other combined lossy/lossless coding schemes such as the emerging JPEG-2000 still image-coding standard PSNR improvements up to 3 dB are achieved for a set of standard test images

SPIHT image coding : analysis, improvements and applications.

Image compression plays an important role in image storage and transmission. In the popular Internet applications and mobile communications, image coding is required to be not only efficient but also scalable. Recent wavelet techniques provide a way for efficient and scalable image coding. SPIHT (set partitioning in hierarchical trees) is such an algorithm based on wavelet transform. This thesis analyses and improves the SPIHT algorithm. The preliminary part of the thesis investigates two-dimensional multi-resolution decomposition for image coding using the wavelet transform, which is reviewed and analysed systematically. The wavelet transform is implemented using filter banks, and the z-domain proofs are given for the key implementation steps. A scheme of wavelet transform for arbitrarily sized images is proposed. The statistical properties of the wavelet coefficients (being the output of the wavelet transform) are explored for natural images. The energy in the transform domain is localised and highly concentrated on the low-resolution subband. The wavelet coefficients are DC-biased, and the gravity centre of most octave-segmented value sections (which are relevant to the binary bit-planes) is offset by approximately one eighth of the section range from the geometrical centre. The intra-subband correlation coefficients are the largest, followed by the inter-level correlation coefficients in the middle then the trivial inter-subband correlation coefficients on the same resolution level. The statistical properties reveal the success of the SPIHT algorithm, and lead to further improvements. The subsequent parts of the thesis examine the SPIHT algorithm. The concepts of successive approximation quantisation and ordered bit-plane coding are highlighted. The procedure of SPIHT image coding is demonstrated with a simple example. A solution for arbitrarily sized images is proposed. Seven measures are proposed to improve the SPIHT algorithm. Three DC-level shifting schemes are discussed, and the one subtracting the geometrical centre in the image domain is selected in the thesis. The virtual trees are introduced to hold more wavelet coefficients in each of the initial sets. A scheme is proposed to reduce the redundancy in the coding bit-stream by omitting the predictable symbols. The quantisation of wavelet coefficients is offset by one eighth from the geometrical centre. A pre-processing technique is proposed to speed up the judgement of the significance of trees, and a smoothing is imposed on the magnitude of the wavelet coefficients during the pre-processing for lossy image coding. The optimisation of arithmetic coding is also discussed. Experimental results show that these improvements to SPIHT get a significant performance gain. The running time is reduced by up to a half. The PSNR (peak signal to noise ratio) is improved a lot at very low bit rates, up to 12 dB in the extreme case. Moderate improvements are also made at high bit rates. The SPIHT algorithm is applied to loss less image coding. Various wavelet transforms are evaluated for lossless SPIHT image coding. Experimental results show that the interpolating transform (4, 4) and the S+P transform (2+2, 2) are the best for natural images among the transforms used, the interpolating transform (4, 2) is the best for CT images, and the bi-orthogonal transform (9, 7) is always the worst. Content-based lossless coding of a CT head image is presented in the thesis, using segmentation and SPIHT. Although the performance gain is limited in the experiments, it shows the potential advantage of content-based image coding