Zhihong Yang
 
The literature on wavelet compression are massive. In INSPEC, use "wavelet compression" as key word, I found 169 papers.
In IEEE Bibliographies On-Line(http://www.biblio.ieee.org/biblio/bibmenu.html), I found 107 papers published in journal by key word " wavelet compression".

Paper 1 :

Quantization
- Gray, R.M.; Neuhoff, D.L.
http://ee.stanford.edu/~gray/
Information Theory, IEEE Transactions on
on Pages: 2325 - 2383
October 1998  Vol. 44 Issue: 6  ISSN: 0018-9448

Author's abstract---The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization is modulation and analog-to digital conversion was first recognized during the early development of pulse-code modulation systems, especially in the 1948 paper of Oliver, Pierce and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.

Student's summary:

IEEE Information society was celebrating  the 50th anniversary of information theory with a special issue of IEEE transaction of information theory. The author contributed this long paper to this issue.  It's interesting to know that the origins of Quantization theory is in pulse-code modulation(PCM). Many early discovery were made at Bell labs. Why so many inportant scientific discoverys  and techniqual inventions are made at US or Europe?
I personally knew quantization from Analog-to-digital(A/D) conversion. I didn't really realize that  this concept is basicly the same as classification until I took this course. So K-means, Isodata, LBG vector quantization, and Learning vertor quantization have many property in common. I didn't realize the position of quantization in compression until I was coding JPEG and EZW.
The basic mathematic method applied in this area are funcational analysis and signal processing.
 

Paper 2:

A Java-based MPEG-4 like video codec
- Dung-Yung Liu; Chien-Wu Tsai; Ja-Ling Wu
Dept. of Comput. Sci. & Inf. Eng., Nat. Taiwan Univ., Taipei, Taiwan
Consumer Electronics, IEEE Transactions on
on Pages: 200 - 205
Feb. 1998  Vol. 44  Issue: 1    ISSN: 0098-3063

Author's Abstract:
The MPEG-4 specification was developed in response to the growing need for a coding method that can facilitate dynamic access to audio-visual objects for various applications such as digital storage media, Internet, various     forms of wired or wireless communication etc. Although the specification is still in the working draft stage, the     concepts and technologies of the specification are very encouraging and will inspire a lot of creative works in     multimedia applications. This paper is devoted to the software implementation of the video part of MPEG-4. We     develop a prototype of MPEG-4 like video encoder and a prototype of Java-based video decoder, which can be     executed on the Internet, in the client-server model by using Java Applet. The prototype can show the strong     functionality of MPEG-4 that includes user interactivity and object scalability, etc.

Student's summary:

Java is slower than C or C++, besides that it has so many good properties that on other language can replace. It can be execurated  everywhere in internet. It has built-in support in displaying image. This properties make academic communications
between scholars, students so easy and effective.  The above paper give us a good example. Unfortunately, I can't find UNL address of their applet.
 

Paper 3:

Multimedia and multimedia communication: a tutorial
- Chwan-Hwa Wu; Irwin, J.D.
Dept. of Electr. Eng., Auburn Univ., AL, USA
Industrial Electronics, IEEE Transactions on
on Pages: 4 - 14
 Feb. 1998 Vol. 45  Issue: 1  ISSN: 0278-0046

Abstract:

 This paper presents, in a tutorial fashion, the important features of multimedia technology. The specific areas addressed are multimedia and compression standards, computer networks, multimedia transport, and some specific applications employed by industry to date. Multimedia and the effective and efficient communication of multimedia using compression and networks are fused together in this tutorial in an attempt to demonstrate the tight coupling which exists between these two interrelated technologies. First, the techniques and properties inherent in both multimedia and compression standards are presented. Then, the important characteristics of the major local and wide area networks are summarized. Next, the communication techniques for the transport of video and video conferencing are discussed. The new strategies employed to connect homes through cable TV and the telephone companies, as well as the new Ethernet technologies, are also described. Finally, some modern applications of multimedia communication derived from the automotive industry are used to describe the use of this technology in design, manufacturing, and sales.

Student's summary:

Multimedia and Mulitmedia communication are hot perfit growth points as well as hot researh areas. It's amazaing that so many standards, techniques and products are developed in these years.  This areas are also high integrated and interdisciplinary. What has been achieved so far is encouraging. But,what hasn't been achieved can excite more research.

Paper 4:
Visibility of wavelet quantization noise
- Watson, A.B.; Yang, G.Y.; Solomon, J.A.; Villasenor, J.
NASA Ames Res. Center, Moffett Field, CA, USA
Image Processing, IEEE Transactions on
on Pages: 1164 - 1175
Aug. 1997 Vol. 6 Issue: 8  ISSN: 1057-7149

Abstract:
The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression, measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact
that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the
corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r*power(2,-lambda). where r is the display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection  thresholds that is a action of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model  may also be used as     the basis for adaptive quantization schemes.

Student's summary:

The author derived the spaital frequency f of wavelet decomposition lambda is f=r*power(2,lambda), which r is display resolution by bixels/degree.  lambda is the level of wavelet decomposition.  The author use human being's eye to evaluate the effect of quantization noise, then construct a methematical model for DWT noise detection thresholds. This model is used to calculate perceptually lossless quantization matrix. Based on this matrix, the author can get better compression redio with perceptually lossless.

http://www.icsl.ucla.edu/~ipl/papers.html

 
Paper 5:
A wavelet-based analysis of fractal image compression
- Davis, G.M.
Dept. of Math., Dartmouth Coll., Hanover, NH, USA
Image Processing, IEEE Transactions on
on Pages: 141 - 154
Feb. 1998 Vol. 7 Issue: 2 ISSN: 1057-7149
Abstract:

Why does fractal image compression work? What is the implicit image model underlying fractal block coding?     How can we characterize the types of images for which fractal block coders will work well? These are the central     issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression     schemes. Within this framework we are able to draw upon insights from the well-established transform coder     paradigm in order to address the issue of why fractal block coders work. We show that fractal block coders of  the form introduced by Jacquin (1992) are Haar wavelet subtree quantization schemes. We examine a   generalization of the schemes to smooth wavelets with additional vanishing moments. The performance of our  generalized coder is comparable to the best results in the literature for a Jacquin-style coding scheme. Our wavelet  framework gives new insight into the convergence properties of fractal block coders, and it leads us to develop an  unconditionally convergent scheme with a fast decoding algorithm. Our experiments with this new algorithm  indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero  trees. Finally, our framework reveals some of the fundamental limitations of current fractal compression schemes.

student's summary:

Fractal block coder is the relative of wavelet transform coder, though it is not as popular as latter.  The author introduce a new wavelet based framework for analyzing block-based fractal compression schemes. His analysis is based on wavelet analog of fractal block coding.

http://www.cs.dartmouth.edu/~gdavis/wavelet/wavelet.html
 
 
 

Paper 6:
A new method of robust image compression based on the embedded zerotree wavelet algorithm
- Creusere, C.D.
Weapons Div., Naval Air Warfare Center, China Lake, CA, USA
Image Processing, IEEE Transactions on
on Pages: 1436 - 1442
Oct. 1997 Vol. 6 Issue: 10 ISSN: 1057-7149

Abstract:
We propose a wavelet-based image compression algorithm that achieves robustness to transmission errors by     partitioning the transform coefficients into groups and independently processing each group using an embedded     coder. Thus, a bit error in one group does not affect the others, allowing more uncorrupted information to reach     the decoder.

Student's summary:
The author partitioned the wavelet cofficient to 4( or power of 4) groups, each group  consists of elements that can be included in the same zero tree. Each group is processed by EZW encoder to become bit stream. Those bitstreams are interleaved before transmitted to decoder. Thus the robustness is improved. Since once a bit error is happened, only the data in this group is effected, other groups won't be effected.

But the author's understanding to zero-tree is not the same as the concept in Shapiro's paper. I doubt if he can still get same compression performance based on his understaning of zero-tree.  In Shapiro's paper, only 3 ( or power of 3)zero-trees is possible. They are HL,LH,and HH subband. LL subband is consisted in inerative way..

Paper 7:
Image compression based on fuzzy algorithms for learning vector quantization
and wavelet image decomposition
- Karayiannis, N.B.; Pai, P.; Zervos, H.
Dept. of Electr. Eng. & Comput. Eng., Houston Univ., TX, USA
Image Processing, IEEE Transactions on
on Pages: 1223 - 1230
Aug. 1998  Vol. 7  Issue: 8  ISSN: 1057-7149
Abstract:
This paper evaluates the performance of an image compression system based on wavelet-based subband    decomposition and vector quantization. The images are decomposed using wavelet filters into a set of subbands    with different resolutions corresponding to different frequency bands. The resulting subbands are vector quantized
using the Linde-Buzo-Gray (1980) algorithm and various fuzzy algorithms for learning vector quantization  (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive neural     network through an unsupervised learning process. The quality of the multiresolution codebooks designed by     these algorithms is measured on the reconstructed images belonging to the training set used for multiresolution     codebook design and the reconstructed images from a testing set.

Student's summary:

The basic idea in this paper is to quantize the wavelet coffiecients by multiresolution code book generated by FALVQ( fuzzy algorithms for learning vector quantization). This algorithm performs vector quantization by updating all prototypes of competitive neural network through an unsupervised learning process. The updating formula is  devived in their paper about neural network( IEEE Transaction on Neural Networks, vol. 8 pp. 206-217; IEEE Transaction on Neural Networks, vol. 7, pp.1196-1211). The authors concluded that FALVQ algorithms tested performed equally well or even better especially at high compression ratios than LBG algorithm. Compared with vector quantization applied on the original image data, the wavelet-based subband decomposition improved dramatically the quality of the reconstructed images within the trainning set. The author also said that the bit allocation strategy employed was even more important than the particular wavelet filter used for image decomposition.

Paper 8:
A zerotree wavelet video coder
- Martucci, S.A.; Sodagar, I.; Chiang, T.; Ya-Qin Zhang
David Sarnoff Res. Center, Princeton, NJ, USA
Circuits and Systems for Video Technology, IEEE Transactions on
on Pages: 109 - 118
Feb. 1997 Vol. 7 Issue: 1 ISSN: 1051-8215
Abstract:
This paper describes a hybrid motion-compensated wavelet transform coder designed for encoding video at very
low bit rates. The coder and its components have been submitted to MPEG-4 to support the functionalities of     compression efficiency and scalability. Novel features of this coder are the use of overlapping block motion     compensation in combination with a discrete wavelet transform followed by adaptive quantization and zerotree     entropy coding, plus rate control. The coder outperforms the VM of MPEG-4 for coding of I-frames and   matches the performance of the VM for P-frames while providing a path to spatial scalability, object scalability, and bitstream scalability.

Student's summary:

The algorithm does not produce an embedded bitstream as EZW does, but by sacrificing the embedded property, this scheme gains flexibility and other advantages over EZW coding, including substantial improvement in coding efficiency.

Zero Tree Entropy coding differs from EZW in four major ways.1)quantization is explieit instead of implicit and can be performed distinct from the zerotree growing process or can be incorporated into the process, thereby making it possible to adjust the quantization according to where the transform coefficient lies and what it represents in the frame; 2) cofficient scanning, tree growing, and coding are done in one pass instead of bit-plane-by-bit-plane; 3) coeffieient scanning is changed from subband-by-subband to a depth-first traversal of each tree; and 4) the alphabet of symbols for classifing the tree nodes is changed to one that performs significantly better for very low bit-rate encoding of video. 
 

Paper 9:
Scalable coding of very high resolution video using the virtual zerotree
- Qi Wang; Ghanbari, M.
Dept. of Electron. Syst. Eng., Essex Univ., Colchester, UK
Circuits and Systems for Video Technology, IEEE Transactions on
on Pages: 719 - 727
Oct. 1997 Vol. 7 Issue: 5  ISSN: 1051-8215

Abstract:

Coding of HDTV and super high definition video requires not only high performance compression but also   compatibility and scalability to satisfy transmission channels of various speeds and capacity and receivers working
at different resolutions. A compatible and scalable coding scheme has been developed for these video signals.     Wavelet decomposition is performed such that the low frequency band is of common intermediate format (CIF)     order, which forms a low-resolution core of the full-sized video and is coded by MPEG. The high-frequency  wavelet coefficients are coded by the proposed virtual zerotree which encodes the wavelet coefficients more  efficiently than the simple zerotree. Also embedded in the scheme is the hierarchical motion compensation that  gives high performance with a large capable compensation range, requires minimum computation, and reduces  overhead
motion information.

Student's summary:
The idea is straight forward.  In hybrid MPEG/wavelet coding of high quality video, The LL band is fed into MPEG coder, there are too many clustered zero tree roots due to the relatively large size of the top-stage subbands. The author constructed a virtual zero tree which the LL band are filled with 0. So the cluster zero tree roots can be replaced by one zero tree root in upper level.
As a consequence, the efficiency of the EZW coder is greatly reduced.
 

Paper 10:

Embedded Image Coding Using Zerotrees of Wavelet Cofficients
Jerome M. Shapiro
Signal processing, IEEE transactions
Dec. 1993 Vol.41 Issue 12

Abstract:
The embedded zerotree wavelet algorithm(EZW) is a simple, yet remarkable effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code. The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image. Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metirc to be met exactly. Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream. In addition to producing a fully embedded bit stream, EZW consistently producing a fully embedded bit stream, EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images. Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source.
The EZW algorithm is based on four key concepts:1)a discrete wavelet transform or hierarchical subband decomposition, 2) prediction of the absence of significant imformation across scales by exploiting the self-similarity inherent in images, 3) entropy-coded successive-approximation quantization, and 4) universal lossless data compression which is achieved via adaptive arithmetic coding.

Student's summary:
This paper has been cited over thousands times since it published. The idea is simple and beautiful. But to get accuate understanding is not easy work.  I have seen wrong understanding on published IEEE journal paper. The encoder  programming is based on iterative algorithm.  This paper offered many space for further research topics, which I give reviews on the  this survey .
 

Paper 11:

Analysis based coding of image transform and subband coefficients.
V. R. Algazi and R. R. Estes
Digital Image Processing XVII, volume 2564 of Proc. of the SPIE, pages 11-21, 1995.
http://info.cipic.ucdavis.edu/scripts/reportPage?95-05
 

Abstract:

Image coding requires an effective representation of images to provide dimensionality reduction, a quantization strategy to maintain image quality, and finally the error free encoding of quantized coefficients. In the coding of quantized coefficients, Huffman coding and arithmetic coding have been used most commonly and are suggested as alternatives in the JPEG standard. In some recent work, zerotree coding has been proposed as an alternate method, that considers the dependence of of quantized coefficients from subband to subband, and thus appears as a generalization of the context-based approach often used with arithmetic coding.

In this paper, we propose to review these approaches and discuss them as special cases of an analysis based approach to the coding of coefficients. The requirements on causality and computational complexity implied by arithmetic and zero-tree coding will be studied and other schemes proposed for the choice of the predictive coefficient contexts that are suggested by image analysis.

Student's summary:

This paper argued that  the zero tree data structure used at EZW algorithm, from a coding efficiency perspective, is of little use.  The author pointed out that the wavelet normalization factor chosen in the forward and inverse wavelet transform is very important.  The author analysed EZW based on "entropy" point of view. He thinks since the possiblity of symbol is unknown, the encoder has to make use of all kinds of method to estimate the possibilty. EZW uses the significance( or insignificance) of its parents and the previous pixel( in the chosen scanning order) to condition zerotree symbols. The author can use somewhat more advanced technique( which I failed to understand) to more accurately condition the possibility. Such that he can get better result than EZW.  I think the author failed to know the advantage of EZW exists in it's effective presentation of self-similarity of wavelet cofficients. His analysis is based on traditional information theory, he didn't give us a detailed example as Shapiro did in the paper. The above made it is difficult to read his paper.