An image multiresolution representation for lossless and lossy compression

L(infinity) constrained high-fidelity image compression via adaptive context modeling

In this paper, we study high-fidelity image compression with a given tight L(infinity) bound. We propose some practical adaptive context modeling techniques to correct prediction biases caused by quantizing prediction residues, a problem common to the existing DPCM-type predictive near-lossless image coders. By incorporating the proposed techniques into the near-lossless version of CALIC that is considered by many as the state-of-the-art algorithm, we were able to increase its PSNR by 1 dB or more and/or reduce its bit rate by 10% or more, more encouragingly, at bit rates around 1.25 bpp or higher, our method obtained competitive PSNR results against the best L(2)-based wavelet coders, while obtaining much smaller L(infinity) bound.

Lossless coding of multichannel signals using optimal vector hierarchical decomposition

A methodology is presented for the optimal construction of multichannel reduced pyramids by selecting the interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid. The general optimization methodology is applied for the optimization of pyramids for the compression of electrocardiographic signals and RGB colored images.

Nonlinear multiresolution signal decomposition schemes--part II: morphological wavelets

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens (1995, 1996, 1998). The aim of this paper, which is a sequel to a previous paper devoted exclusively to the pyramid transform, is to present an axiomatic framework encompassing most existing linear and nonlinear wavelet decompositions. Furthermore, it introduces some, thus far unknown, wavelets based on mathematical morphology, such as the morphological Haar wavelet, both in one and two dimensions. A general and flexible approach for the construction of nonlinear (morphological) wavelets is provided by the lifting scheme. This paper briefly discusses one example, the max-lifting scheme, which has the intriguing property that preserves local maxima in a signal over a range of scales, depending on how local or global these maxima are.

Optimal progressive lossless image coding using reduced pyramids with variable decimation ratios

This correspondence introduces a novel method for the construction of extended reduced pyramids with rational decimation ratios from stage to stage. It is shown that this construction produces more accurate interpolation, and thus more efficient lossless compression, than conventional reduced pyramids.

Wavelet image compression--the quadtree coding approach

Perfect reconstruction, quality scalability, and region-of-interest coding are basic features needed for the image compression schemes used in telemedicine applications. This paper proposes a new wavelet-based embedded compression technique that efficiently exploits the intraband dependencies and uses a quadtree-based approach to encode the significance maps. The algorithm produces a losslessly compressed embedded data stream, supports quality scalability, and permits region-of-interest coding. Moreover, experimental results obtained on various images show that the proposed algorithm provides competitive lossless/lossy compression results. The proposed technique is well suited for telemedicine applications that require fast interactive handling of large image sets, over networks with limited and/or variable bandwidth.

A progressively predictive image pyramid for efficient lossless coding

A low entropy pyramidal image data structure suited for lossless coding and progressive transmission is proposed in this work. The new coder, called the progressively predictive pyramid (PPP) is based on the well-known Laplacian pyramid. By introducing inter-resolution predictors into the original Laplacian pyramid, we show that the entropy level in the original pyramid can be reduced significantly. To take full advantage of progressive transmission, a scheme is introduced to create the predictor adaptively, thus eliminating the need to transmit the predictor and reducing the coding overheads. A method for designing the predictor is presented. Numerical results show that PPP is superior to traditional approaches to pyramid generation in the sense that the pyramids generated by PPP always have significantly lower entropy values.

Image compression via joint statistical characterization in the wavelet domain

We develop a probability model for natural images, based on empirical observation of their statistics in the wavelet transform domain. Pairs of wavelet coefficients, corresponding to basis functions at adjacent spatial locations, orientations, and scales, are found to be non-Gaussian in both their marginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitudes are highly correlated. We propose a Markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties, and show that it accounts for the statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of the 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 nonadaptive arithmetic encoder that utilizes conditional 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. Despite the simplicity of the model, the rate-distortion performance of the coder is roughly comparable to the best image coders in the literature.

Significance-linked connected component analysis for wavelet image coding

Recent success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation. There have been several very competitive wavelet coders developed, namely, Shapiro's (1993) embedded zerotree wavelets (EZW), Servetto et al.'s (1995) morphological representation of wavelet data (MRWD), and Said and Pearlman's (see IEEE Trans. Circuits Syst. Video Technol., vol.6, p.245-50, 1996) set partitioning in hierarchical trees (SPIHT). We develop a novel wavelet image coder called significance-linked connected component analysis (SLCCA) of wavelet coefficients that extends MRWD by exploiting both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. Extensive computer experiments on both natural and texture images show convincingly that the proposed SLCCA outperforms EZW, MRWD, and SPIHT. For example, for the Barbara image, at 0.25 b/pixel, SLCCA outperforms EZW, MRWD, and SPIHT by 1.41 dB, 0.32 dB, and 0.60 dB in PSNR, respectively. It is also observed that SLCCA works extremely well for images with a large portion of texture. For eight typical 256x256 grayscale texture images compressed at 0.40 b/pixel, SLCCA outperforms SPIHT by 0.16 dB-0.63 dB in PSNR. This performance is achieved without using any optimal bit allocation procedure. Thus both the encoding and decoding procedures are fast.

A review of compression methods for medical images in PACS

As an introduction to Section C2 (medical imaging) of track C (Images and PACS) of MIE '97, an appropriate and timely topic concerns the coding for the transmission of medical images in PACS. Speed limitations of existing networks along with the explosive growth of image modalities with extremely high volume outputs have combined to make the issue of medical image coding one of the key considerations in the design of future PACS systems. Both lossless and lossy compression schemes are reviewed and compared, and the compression demands are presented of the main digital medical image modalities.

Rounding transform and its application for lossless pyramid structured coding

A new transform, called the rounding transform (RT), is introduced in this paper. This transform maps an integer vector onto another integer vector by using weighted average and difference filters followed by a rounding operation. The RT can be applied to lossless pyramid structured coding with various elementary block sizes and filters. In addition, it generalizes other mean based lossless pyramid structured coding schemes.

Joint space-frequency segmentation using balanced wavelet packet trees for least-cost image representation

We examine the question of how to choose a space varying filterbank tree representation that minimizes some additive cost function for an image. The idea is that for a particular cost function, e.g., energy compaction or quantization distortion, some tree structures perform better than others. While the wavelet tree represents a good choice for many signals, it is generally outperformed by the best tree from the library of wavelet packet frequency-selective trees. The double-tree library of bases performs better still, by allowing different wavelet packet trees over all binary spatial segments of the image. We build on this foundation and present efficient new pruning algorithms for both one- and two-dimensional (1-D and 2-D) trees that will find the best basis from a library that is many times larger than the library of the single-tree or double-tree algorithms. The augmentation of the library of bases overcomes the constrained nature of the spatial variation in the double-tree bases, and is a significant enhancement in practice. Use of these algorithms to select the least-cost expansion for images with a rate-distortion cost function gives a very effective signal adaptive compression scheme. This scheme is universal in the sense that, without assuming a model for the signal or making use of training data, it performs very well over a large class of signal types. In experiments it achieves compression rates that are competitive with the best training-based schemes.