William A. Pearlman

A new, fast, and efficient image codec based on set partitioning in hierarchical trees

Embedded zerotree wavelet (EZW) coding, introduced by Shapiro (see IEEE Trans. Signal Processing, vol.41, no.12, p.3445, 1993), is a very effective and computationally simple technique for image compression. We offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood. These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform. Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW. The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods. In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by the arithmetic code.

An image multiresolution representation for lossless and lossy compression

We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.

Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT)

We propose a low bit-rate embedded video coding scheme that utilizes a 3-D extension of the set partitioning in hierarchical trees (SPIHT) algorithm which has proved so successful in still image coding. Three-dimensional spatio-temporal orientation trees coupled with powerful SPIHT sorting and refinement renders 3-D SPIHT video coder so efficient that it provides comparable performance to H.263 objectively and subjectively when operated at the bit rates of 30 to 60 kbits/s with minimal system complexity. Extension to color-embedded video coding is accomplished without explicit bit allocation, and can be used for any color plane representation. In addition to being rate scalable, the proposed video coder allows multiresolutional scalability in encoding and decoding in both time and space from one bit stream. This added functionality along with many desirable attributes, such as full embeddedness for progressive transmission, precise rate control for constant bit-rate traffic, and low complexity for possible software-only video applications, makes the proposed video coder an attractive candidate for multimedia applications.

Wavelet compression of ECG signals by the set partitioning in hierarchical trees algorithm

A wavelet electrocardiogram (ECG) data codec based on the set partitioning in hierarchical trees (SPIHT) compression algorithm is proposed in this paper. The SPIHT algorithm (A. Said and W.A. Pearlman, IEEE Trans. Ccts. Syst. II, vol. 6, p. 243-50, 1996) has achieved notable success in still image coding. The authors modified the algorithm for the one-dimensional case and applied it to compression of ECG data. Experiments on selected records from the MIT-BIH arrhythmia database revealed that the proposed codec is significantly more efficient in compression and in computation than previously proposed ECG compression schemes. The coder also attains exact bit rate control and generates a bit stream progressive in quality or rate.

Efficient, low-complexity image coding with a set-partitioning embedded block coder

We propose an embedded, block-based, image wavelet transform coding algorithm of low complexity. It uses a recursive set-partitioning procedure to sort subsets of wavelet coefficients by maximum magnitude with respect to thresholds that are integer powers of two. It exploits two fundamental characteristics of an image transform-the well-defined hierarchical structure, and energy clustering in frequency and in space. The two partition strategies allow for versatile and efficient coding of several image transform structures, including dyadic, blocks inside subbands, wavelet packets, and discrete cosine transform (DCT). We describe the use of this coding algorithm in several implementations, including reversible (lossless) coding and its adaptation for color images, and show extensive comparisons with other state-of-the-art coders, such as set partitioning in hierarchical trees (SPIHT) and JPEG2000. We conclude that this algorithm, in addition to being very flexible, retains all the desirable features of these algorithms and is highly competitive to them in compression efficiency.

An embedded wavelet video coder using three-dimensional set partitioning in hierarchical trees (SPIHT)

The SPIHT (set partitioning in hierarchical trees) algorithm by Said and Pearlman (see IEEE Trans. on Circuits and Systems for Video Technology, no.6, p.243-250, 1996) is known to have produced some of the best results in still image coding. It is a fully embedded wavelet coding algorithm with precise rate control and low complexity. We present an application of the SPIHT algorithm to video sequences, using three-dimensional (3D) wavelet decompositions and 3D spatio-temporal dependence trees. A full 3D-SPIHT encoder/decoder is implemented in software and is compared against MPEG-2 in parallel simulations. Although there is no motion estimation or compensation in the 3D SPIHT, it performs measurably and visually better than MPEG-2, which employs complicated motion estimation and compensation.

Embedded and efficient low-complexity hierarchical image coder

We propose an embedded hierarchical image coding algorithm of low complexity. It exploits two fundamental characteristics of an image transform -- the well defined hierarchical structure, and energy clustering in frequency and in space. The image coding algorithm developed here, apart from being embedded and of low complexity, is very efficient and is comparable to the best known low-complexity image coding schemes available today.

Image compression using the spatial-orientation tree

The zero-tree method for image compression, proposed by J. Shapiro (1992), is studied. The method is presented in a more general perspective, so that its characteristics can be better understood. From this analysis, an improved method is proposed, and it is shown that the new method can increase the PSNR up to 1.3 dB over the original method.<<ETX>>

Reversible image compression via multiresolution representation and predictive coding

In this paper a new image transformation suited for reversible (lossless) image compression is presented. It uses a simple pyramid multiresolution scheme which is enhanced via predictive coding. The new transformation is similar to the subband decomposition, but it uses only integer operations. The number of bits required to represent the transformed image is kept small through careful scaling and truncations. The lossless coding compression rates are smaller than those obtained with predictive coding of equivalent complexity. It is also shown that the new transform can be effectively used, with the same coding algorithm, for both lossless and lossy compression. When used for lossy compression, its rate-distortion function is comparable to other efficient lossy compression methods.

SPIHT image compression without lists

A variant of the SPIHT image compression algorithm called no list SPIHT (NLS) is presented. NLS operates without linked lists and is suitable for a fast, simple hardware implementation. NLS has a fixed predetermined memory requirement about 50% larger than that needed for the image alone. Instead of lists, a state table with four bits per coefficient keeps track of the set partitions and what information has been encoded. NLS sparsely marks selected descendant nodes of insignificant trees in the state table in such a way that large groups of predictably insignificant pixels are easily identified and skipped during coding passes. The image data is stored in a one dimensional recursive zig-zag array for computational efficiency and algorithmic simplicity. The performance of the algorithm on standard test images is nearly the same as SPIHT.