Elsevier

Signal Processing

Volume 80, Issue 7, July 2000, Pages 1281-1287
Signal Processing

Multi-iteration wavelet zero-tree coding for image compression

https://doi.org/10.1016/S0165-1684(00)00035-9Get rights and content

Abstract

Here, we present a modification of Shapiro's embedded zerotree wavelet algorithm (EZW) for image codec. Shapiro's technique is based on the wavelet transform and on the self-similarity inherent in images. In the EZW, the wavelet transform (WT) coefficients, which provide a multiresolution representation of the image, are arranged according to their significance across scales using a small symbol set (zerotree (ZT) coding). An analysis of the symbol entropy shows that better compression rates can be obtained when two or more iterations of the original algorithm are combined. Consequently, we proposed a modification of Shapiro's original algorithm which we called multi-iteration EZW designed to optimise the combination of ZT and Huffman coding. We studied the behaviour of the multi-iteration algorithm in terms of image quality and bit-rate for natural and medical images. Our findings show that for a given image quality the multi-iteration algorithms and particularly the two-iteration EZW produce lower bit-rates than Shapiro's. In addition, we suggest that the idea of multi-iteration can be generalised to other techniques based on ZT coding.

Zusammenfassung

In dieser Arbeit stellen wir eine Modifikation von Shapiros eingebettetem Nullbaum-Wavelet-Algorithmus (EZW) für die Bildkodierung vor. Shapiros Verfahren beruht auf der Wavelettransformation und der inhärenten Selbstähnlichkeit von Bildern. In der EZW werden die Koeffizienten der Wavelettransformation (WT), die eine mehrfach auflösende Bilddarstellung ergeben, nach ihrer Signifikanz über die Skalierungen durch die Verwendung einer kleinen Symbolmenge (Nullbaum (ZT) Kodierung) angeordnet. Eine Analyse der Symbolentropie zeigt, daß bessere Kompressionstraten durch die Kombination von zwei oder mehr Iterationen des ursprünglichen Algorithmus erreicht werden können. Deshalb schlagen wir eine Modifikation des ursprünglichen Shapiro-Algorithmus vor, die wir Mehriterationen-EZW nennen und die die Kombination von ZT und Huffman-Kodierung optimiert. Wir untersuchten das Verhalten des Mehriterationen-Algorithmus bezüglich Bildqualität und Bitrate bei natürlichen und medizinischen Bildern. Unsere Ergebnisse zeigen, daß bei vorgegebener Bildqualität die Mehriterationenalgorithmen und insbesondere der zweifach iterierte EZW niedrigere Bitraten ergeben als Shapiros Algorithmus. Zusätzlich schlagen wir vor, die Idee der Mehrfachiteration auf andere Verfahren der ZT-Kodierung zu verallgemeinern.

Résumé

Nous présentons une modification de l'algorithme de Shapiro (Embedded Zerotree Wavelet (EZW)) pour le codage d'images. La technique de Shapiro est basée sur la transformée en ondelettes (WT) et sur l'auto-similarité inhérente à l'image. Les coefficients de la transformée en ondelettes sont organisés selon leur importance à travers les echelles en utilisant un petit ensemble de symboles (codage zerotree (ZT)). Une analyse de l'entropie montre que de meilleurs taux de compression peuvent être obtenus quand on combine deux itérations (ou plus) de l'algorithme original. Par conséquent, nous proposons une modification de l'algorithme original de Shapiro, que nous avons appelée EZW à multi-itérations, et qui a été conçue afin d'optimiser la combinaison de ZT et du codage d'Huffman. Nous avons étudié le comportement de l'algorithme à multi-itérations en fonction de la qualité de l'image et du taux d'erreur par bit et ce pour des images naturelles et médicales. Nous montrons que, pour ue qualité d'image donnée, les algorithmes à multi-itérations (en particulier l'EZW à deux itérations) donnent un taux d'erreur par bit plus petit que celui donné par l'algorithm de Shapiro. Nous suggérons également de généraliser l'idée de multi-itérations à d'autres techniques basées sur le codage ZT.

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.

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