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An image multiresolution representation for lossless and lossy compression. (1996)

by A Said, W A Pearlman
Venue:IEEE T. Image Proc.,
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Wavelet Transforms that Map Integers to Integers

by Robert Calderbank, et al.
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Abstract - Cited by 357 (6 self) - Add to MetaCart
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...ssless image coder and compare the results to the literature. 1. Introduction Wavelets, wavelet packets, and local cosine transforms are used in a variety of applications, including image compression =-=[2, 29, 39, 10, 25]-=-. In most cases, the filters that are used have floating point coefficients. For instance, if one prefers to use orthonormal filters with an assigned number N (N ? 2) of vanishing moments and minimal ...

The JPEG2000 Still Image Coding System: an Overview

by Charilaos Christopoulos, Athanassios Skodras, Touradj Ebrahimi , 2000
"... With the increasing use of multimedia technologies, image compression requires higher performance as well as new features. To address this need in the specific area of still image encoding, a new standard is currently being developed, the JPEC2000. It is not only intended to provide rate-distortion ..."
Abstract - Cited by 259 (2 self) - Add to MetaCart
With the increasing use of multimedia technologies, image compression requires higher performance as well as new features. To address this need in the specific area of still image encoding, a new standard is currently being developed, the JPEC2000. It is not only intended to provide rate-distortion and subjective image quality performance superior to existing standards, but also to provide features and functionalities that current standards can either not address efficiently or in many cases cannot address at all. Lossless and lossy compression, embedded lossy to lossless coding, progressive transmission by pixel accuracy and by resolution, robustness to the presence of bit-errors and region-of-interest coding, are some representative features. It is interesting to note that JPEG2000 is being designed to address the requirements of a diversity of applications, e.g. Internet, color facsimile, printing, scanning, digital photography, remote sensing, mobile applications, medical imagery, digital library and E-commerce.

Image compression via joint statistical characterization in the wavelet domain

by Robert W. Buccigrossi, Eero P. Simoncelli , 1997
"... 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 decorrelate ..."
Abstract - Cited by 238 (24 self) - Add to MetaCart
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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... eight spatial neighbors and the coefficient at a coarser scale. Chrysafis and Ortega [4] switch between multiple probability models depending on values of neighboring coefficients. Said and Pearlman =-=[23]-=- use a predictive scheme to give high-quality zerotree coding results, and Wu and Chen [37] have extended the EZW coder to use local coefficient “contexts”. LoPresto et. al. [13] model the coefficient...

The JPEG2000 still image compression standard

by Athanassios Skodras, Charilaos Christopoulos, Touradj Ebrahimi - IEEE Signal Proc. Mag , 2001
"... The development of standards (emerging and established) by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electrotechnical Commission (IEC) for audio, image, and video, for both transmission and storage, has led to wo ..."
Abstract - Cited by 180 (11 self) - Add to MetaCart
The development of standards (emerging and established) by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electrotechnical Commission (IEC) for audio, image, and video, for both transmission and storage, has led to worldwide activity in developing hardware and software systems and products applicable to a number of diverse disciplines [7], [22], [23], [55], [56], [73]. Although the standards implicitly address the basic encoding operations, there is freedom and flexibility in the actual design and development of devices. This is because only the syntax and semantics of the bit stream for decoding are specified by standards, their main objective being the compatibility and interoperability among the systems (hardware/software) manufactured by different companies. There is, thus, much room for innovation and ingenuity. Since the mid 1980s, members from both the ITU and the ISO have been working together to establish a joint international standard for the compression of grayscale and color still images. This effort has been known as JPEG, the Joint
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... The ROI general scaling-based method can be applied to any embedded coding scheme, as for example, the embedded DCT based coders [52], the various wavelet filters [31] and the zero-tree coders [57], =-=[58]-=-, [61]. Scalability Scalable coding of still images means the ability to achieve coding of more than one qualities and/or resolutions simultaneously. Scalable image coding involves generating a coded ...

Statistical Models for Images: Compression, Restoration and Synthesis

by Eero Simoncelli - In 31st Asilomar Conf on Signals, Systems and Computers , 1997
"... this paper, we examine the problem of decomposing digitized images, through linear and/or nonlinear transformations, into statistically independent components. The classical approach to such a problem is Principal Components Analysis (PCA), also known as the Karhunen-Loeve (KL) or Hotelling transfor ..."
Abstract - Cited by 161 (30 self) - Add to MetaCart
this paper, we examine the problem of decomposing digitized images, through linear and/or nonlinear transformations, into statistically independent components. The classical approach to such a problem is Principal Components Analysis (PCA), also known as the Karhunen-Loeve (KL) or Hotelling transform. This is a linear transform that removes second-order dependencies between input pixels. The most well-known description of image statistics is that their power spectra take the form of a power law [e.g., 20, 11, 24]. Coupled with a constraint of translationinvariance, this suggests that the Fourier transform is an appropriate PCA representation. Fourier and related representations are widely used in image processing applications.
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...r image compression. Although many image coders do not incorporate an explicit probability model, a number of recent algorithms make use of joint statistical regularities between wavelet coefficients =-=[19, 27, 22, 26, 15, 25, 6, 32, 16]-=-. We have constructed two coders called EPWIC [4, 29, 3] based directly on the probability models described in sections 1 and 2. In both coders, subband coefficients are encoded one bitplane at a time...

Nonlinear wavelet transforms for image coding via lifting

by Roger L. Claypoole, Jr., Geoffrey M. Davis, Wim Sweldens, Richard G. Baraniuk , 2003
"... We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We al ..."
Abstract - Cited by 104 (3 self) - Add to MetaCart
We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.
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...e currently do not know how to make adaptive versions of general wavelet transforms. A second example of a non-linear lifting construction is the integer-to-integer S+P transform of Said and Pearlman =-=[16]-=-, shown in Figure 5. The outputs h[n] and c[n] of the S algorithm are computed as: h[n] = x o [n] x e [n] (9) c[n] = x e [n] +Q (h[n]=2) (10) where Q is a round-off operator to ensure the transform i...

An overview of JPEG 2000

by Michael W. Marcellin, Michael J. Gormish, Ali Bilgin, Martin P. Boliek - in Proc. IEEE Data Compression Conf., Snowbird, UT , 2000
"... JPEG-2000 is an emerging standard for still image compression. This paper provides a brief history of the JPEG-2000 standardization process, an overview of the standard, and some description of the capabilities provided by the standard. Part I of the JPEG-2000 standard specifies the minimum complian ..."
Abstract - Cited by 95 (2 self) - Add to MetaCart
JPEG-2000 is an emerging standard for still image compression. This paper provides a brief history of the JPEG-2000 standardization process, an overview of the standard, and some description of the capabilities provided by the standard. Part I of the JPEG-2000 standard specifies the minimum compliant decoder, while Part II describes optional, value-added extensions. Although the standard specifies only the decoder and bitstream syntax, in this paper we describe JPEG-2000 from the point of view of encoding. We take this approach, as we believe it is more amenable to a compact description more easily understood by most readers. 1
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...uantization was included in VM 2. For integer wavelets, scalar quantization with step size 1 was employed (i.e., no quantization), which allowed progression to lossless in the manner of CREW or SPIHT =-=[16]-=- (using the S+P transform). Rate control for integer wavelets was accomplished by embedding, and lossless compression was available naturally from the fully decoded embedded bitstream. Other features,...

Lossless image compression using integer to integer wavclct transforms

by W Sweldens Daubechies, B Yeo - IEEE Inremarional Conference on lmuge Processing , 1997
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Abstract - Cited by 65 (0 self) - Add to MetaCart
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... The oldest integer to integer wavelet transform is the S transform [1], which is an integer version of the Haar transform: d1;l = s0;2l+1 \Gamma s0;2l s1;l = s1;l + bd1;l =2c : (1) Said and Pearlman =-=[2]-=- further proposed the S+P transform (S transform + Prediction) in which linear prediction is performed on the lowpass coefficients s1;l to generate a new set of highpass coefficients after an S transf...

Multiresolution signal decomposition schemes. Part 1: Linear and morphological pyramids

by John Goutsias, Henk J. A. M. Heijmans - IEEE TRANSACTIONS ON IMAGE PROCESSING , 2000
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Abstract - Cited by 62 (8 self) - Add to MetaCart
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...iterature for several years, and has been successfully used in medical imaging for lossless compression [33]. During the years, several modifications and generalizations have been proposed, e.g., see =-=[34]-=-. We should point out here that certain continuity issues may arise in the case of an infinite-level wavelet decomposition scheme. However, these issues, which become manifest in the case of infinite ...

37 other authors

by Michael D. Adams, Rabab K. Ward, Michael D. Adams, Rabab K. Ward, Michael D. Adams, Rabab K. Ward - Science , 1995
"... Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric exte ..."
Abstract - Cited by 59 (1 self) - Add to MetaCart
Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric extension. One of these families is then studied in detail, and several interesting results concerning its member transforms are presented. In addition, some new reversible ITI structures are derived that are useful in conjunction with techniques like symmetric extension. Lastly, the relationship between symmetric extension and per-lifting-step extension is explored, and some new results are obtained in this regard.
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