Multi-iteration wavelet zero-tree coding for image compression
Introduction
Image storage and transmission pose an important problem to the development of intelligent communication systems due to memory and bandwidth requirements. Consequently, many different image compression techniques have been devised during the last few decades. Although lossless or reversible schemes are preferable, the achieved compression ratios are relatively low which makes necessary the use of lossy (irreversible) schemes, allowing some distortion in the reconstructed images. The efficiency of a coder can be defined as the image quality for a given bit-rate which is generally increased at the cost of computational complexity [2]. One exception is the embedded zerotree wavelet (EZW) introduced by Shapiro [5] whose efficiency is similar to other compression techniques but yet, it is comparatively simple. This technique addresses the two-fold problem of obtaining the best image quality for a given rate and accomplishing this task in an embedded fashion, i.e., in such a way that all encodings of the same image at lower bit-rates are embedded in the beginning of the bit stream for the target bit-rate. The EZW algorithm is based on a wavelet transform [6] which provides a compact multiresolution representation of the image, followed by the prediction of the absence of significant information across scales due to the self-similarity inherent in images [3]. The wavelet coefficients are organised into significance maps where they are partially ordered in magnitude by comparison to a set of decreasing thresholds. Subsequent zero-tree (ZT) coding results in a multiresolution representation of the significance maps by a small symbol set. After ZT coding, insignificant coefficients across scales are coded as part of exponentially growing trees by a unique symbol, the zerotree root (ZTR). Further improvement in compression rate is achieved by entropy coding the symbol string.
An entropy analysis over the symbol string reveals that most of the symbols being ZTRs, significant improvement can be achieved by combining several iterations while diversifying the ZTR, providing new representations better adapted to the subsequent entropy coding. Thus, we developed a modified version of the basic algorithm that we term, multi-iteration EZW. Details of both algorithms are given in the next section, while the results obtained for two images (Lena and a thorax radiography) are presented afterwards. A summary and conclusions are presented last.
Section snippets
Algorithms
The EZW algorithm is based on the construction of two lists for a given image previously decorrelated with a wavelet transform. In the first list, called the dominant list, the information about the significance of a coefficient is coded, while in the second or significant list, only the values for the significant coefficients are kept up to a given degree of precision. The difference between Shapiro's original algorithm and our modification lies in the way the significance is determined and
Experiments and results
Performances of the original and modified algorithms and of the standard JPEG have been compared for two 8 bpp images: a standard 512×512 Lena and a 512×512 thorax radiography. Both images were first transformed using a 6-scale biorthogonal wavelet [1] and then, coded with each of the algorithms described above followed by an adapted Huffman coding. After an entropy analysis, we found that the best performance is obtained when only two iterations are combined. We found that for three or more
Summary and conclusions
We present a modified version of the embedded zerotree wavelet basic algorithm introduced by Shapiro that can be applied to natural and medical image codec. The multi-iteration algorithm shows a clear advantage in the compression ratio achieved for a given PSNR over the traditional EZW and it works at higher speed. Preliminary results in medical images show that our algorithm gives better visual qualities than other lossy methods traditionally used. It has also the advantage common to embedded
Acknowledgements
This research has been supported by the Comisión Interministerial de Ciencia y Tecnologı́a (Spain) under grant TIC96-0500-C10-05.
References (6)
Orthonormal bases of compactly supported wavelets
Commun. Pure Appl. Math.
(1988)Speech and image coding (special issue)
IEEE J. Selected Areas Common.
(1992)Scale invariance and self-similar wavelet transforman analysis of natural images and mammalian visual systems
Cited by (13)
ECG signal compression by multi-iteration EZW coding for different wavelets and thresholds
2007, Computers in Biology and MedicineEmpirical evaluation of EZW and other encoding techniques in the wavelet-based image compression domain
2015, International Journal of Wavelets, Multiresolution and Information Processing2D-discrete walsh wavelet transform for image compression with arithmetic coding
2013, 2013 4th International Conference on Computing, Communications and Networking Technologies, ICCCNT 2013Performance comparison of arithmetic and Huffman coder applied to EZW codec
2012, ICPCES 2012 - 2012 2nd International Conference on Power, Control and Embedded Systems