IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 11, NO. 11, NOVEMBER 2002 1271 Context-Based Entropy Coding of Block Transform Coefficients for Image Compression Chengjie Tu, Student Member, IEEE, and Trac D. Tran, Member, IEEE Abstract—It has been well established that state-of-the-art wavelet image coders outperform block transform image coders in the rate-distortion (R-D) sense by a wide margin. Wavelet-based JPEG2000 is emerging as the new high-performance international standard for still image compression. An often asked question is: how much of the coding improvement is due to the transform and how much is due to the encoding strategy? Current block transform coders such as JPEG suffer from poor context mod- eling and fail to take full advantage of correlation in both space and frequency sense. This paper presents a simple, fast, and efficient adaptive block transform image coding algorithm based on a combination of prefiltering, postfiltering, and high-order space–frequency context modeling of block transform coefficients. Despite the simplicity constraints, coding results show that the proposed coder achieves competitive R-D performance compared to the best wavelet coders in the literature. Index Terms—Adaptive entropy coding, block transform, context modeling, DCT, image coding, JPEG, postfiltering, prefiltering. I. INTRODUCTION A N IMAGE CODING algorithm generally involves a transformation to compact most of the energy of the input image into a few transform coefficients which are then quan- tized and entropy encoded. The two popular transformation approaches for image compression are the block transform and the wavelet transform. The block-based approach partitions the input image into small nonoverlapped blocks; each of them is then mapped into a block of coefficients via a particular block transform usually constructed from local cosine/sine bases. Most popular amongst block transforms for visual data is the type-II discrete cosine transform (DCT) [1] and the block size is commonly set to 8 8. Block DCT coding is the basis of many international multimedia compression standards from JPEG for still images to the MPEG family for video sequences. Low-complexity and good energy compaction within a data block are two main reasons why the DCT has been popular. Unfortunately, at low bit rates, block-based systems suffer from the notorious blocking artifacts, i.e., discontinuities at the block boundaries resulting from reconstruction mismatches. Unlike the block transform approach, the wavelet transform approach treats the input signal globally and avoids blocking Manuscript received December 17, 2001; revised July 11, 2002. This work was supported by the NSF under CAREER Grant CCR-0093262. The associate editor coordinating the review of this manuscript and approving it for publica- tion was Dr. Nasir Memon. The authors are with the Department of Electrical and Computer Engi- neering, The Johns Hopkins University, Baltimore, MD 21218 USA (e-mail: cjtu@jhu.edu; trac@jhu.edu). Digital Object Identifier 10.1109/TIP.2002.804279 artifacts by employing overlapped basis functions. (To process high-resolution images, practical implementations partition the input into large data blocks, called tiles, and transform them in- dependently.) The wavelet transform can be interpreted as an iteration of a two-channel filter bank with a certain degree of regularity on its lowpass output. Part of the beauty and power of wavelets is their elegance: complicated tilings of the time–fre- quency plane can be easily achieved by merely iterating a simple two-channel decomposition. Furthermore, a coarse approxima- tion together with detailed wavelet components at different res- olutions allows fast execution of many DSP applications such as image browsing, database retrieval, scalable multimedia de- livery, etc. Since the introduction of the embedded zerotree wavelet (EZW) compression algorithm by Shapiro in 1993 [2], wavelet coding technology has advanced significantly. State-of-the-art wavelet coding algorithms, such as Said and Pearlman’s set partitioning in hierarchical trees (SPIHT) [3], Chrysafis and Or- tega’s context-based entropy coding (C/B) [4], Wu’s embedded conditional entropy coding of wavelet coefficients (ECECOW) [5] and ECECOW with context quantization guided by Fisher discriminant (FD) [6], Hong and Ladner’s group testing for wavelets (GTW) [7], and especially Taubman’s embedded block coding with optimized truncation (EBCOT) [8]—the framework for the current state of the JPEG2000 image com- pression standard [9], give the best R-D performance in the literature. In the meantime, the progress for block transform image coding is limited and the R-D performance gap between the best wavelet coding algorithm and the best block transform coding algorithm is quite large. The success of wavelet coding technology is mainly a result of advanced context modeling and adaptive entropy coding of wavelet coefficients. Good context-based entropy coding well exploits the nature of wavelet coefficients such as multiresolu- tion structure, parent–children relationship, zero clustering, and sign correlation. On the contrary, context based entropy coding of block transform coefficients has not received much attention. The standard method for coding quantized block transform co- efficients is still JPEG’s zigzag scanning and runlength coding technology, whose efficiency at least suffers from: 1) 2-D data is encoded in a 1-D manner; correlation between coefficients in the same block has not been fully exploited; 2) data blocks are coded independently (except for DC prediction) and corre- lation between blocks has been mostly ignored; and 3) too many run-level combinations result in suboptimal entropy coding. Recently, there have been several block-transform-based image coders which use zerotree wavelet coding algorithms such as EZW and SPIHT to encode block transform coefficients 1057-7149/02$17.00 © 2002 IEEE