Embedded zerotree wavelet (EZW) coding,introduced by J. M. Shapiro, is a very effective and computationally simple technique for image compression. Here 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 previosly reported extension of the 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 arithmetic code.

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 in modulation and analog-to-digital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for 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.

We develop a statistical characterization of natural images in the wavelet transform domain. This characterization describes the joint statistics between pairs of subband coefficients at adjacent spatial locations, orientations, and scales. We observe that the raw coefficients are nearly decorrelated, but their magnitudes are highly correlated. A linear magnitude predictor coupled with both multiplicative and additive uncertainties accounts for the joint coefficient statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of this model, we construct an image coder called EPWIC (Embedded Predictive Wavelet Image Coder), in which subband coefficients are encoded one bitplane at a time using a non-adaptive arithmetic encoder that utilizes probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. The rate-distortion performance of the coder compares favorably with the current best image coders in the literature. 1

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The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms Donoho and Johnstone's SureShrink most of the time. The second part

Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation [1, 2]. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all non-zeroed coefficients), and we formalize the problem of optimizing their joint application and we develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive (often...

The growth of new imaging technologies has created a need for techniques that can be used for copyright protection of digital images. Copyright protection involves the authentication of image content and/or ownership and can be used to identify illegal copies of a (possibly forged) image. One approach for copyright protection is to introduce an invisible signal known as a digital watermark in the image. In this paper, we describe digital image watermarking techniques, known as perceptually based watermarks, that are designed to exploit aspects of the human visual system. In the most general sense, any watermarking technique that attempts to incorporate an invisible mark into an image is perceptually based. However, in order to provide transparency (invisibility of the watermark) and robustness to attack, more sophisticated use of perceptual information in the watermarking process is required. Several techniques have been introduced that incorporate a simple visual model in the marking procedure. Such techniques usually take advantage of frequency selectivity and weighing to provide some perceptual criteria in the watermarking process. Even more elaborate visual models are used to develop schemes that not only take advantage of frequency

An orthogonal basis of L 2 which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F. Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other orthogonal basis. In fact, simple thresholding in an unconditional basis works essentially better for recovery and estimation than other methods, period. (Performance is measured in an asymptotic minimax sense.) As an application, we formalize and prove Mallat's Heuristic, which says that wavelet bases are optimal for representing functions containing singularities, when there may be an arbitrary number of singularities, arbitrarily distributed.

In this paper, we propose a low bit-rate embedded video coding scheme that utilizes a threedimensional (3D) 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 3D 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 kilobits per second 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 ...

The SPIHT (set partitioning in hierarchical trees) algorithm by Said and Pearlman is known to have produced some of the best results in still image coding. It is a fully embeded wavelet coding algorithm with precise rate control and low complexity. In this paper is presented 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 3D SPIHT, it performs measurably and visually better than MPEG2, which employs complicated means of motion estimation and compensation.