A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process., vol. 6, no. 8, pp. 1164--1175, Aug. 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....attempt to mimic the multi channel nature of the HVS by transforming an image into a series of subbands prior to quantization. Previous psychophysical studies of wavelet subband quantization have focused on analysis of quantization step sizes and their direct application to compression. In [4], unmasked visibility thresholds were measured for individual wavelet basis functions and for distortions induced by adding uniform noise into single DWT subbands; these data were used to compute at threshold quantizer step sizes for individual subbands. In [5] suprathreshold quantizer step ....

.... have found probability summation for compound targets composed of well separated components that differed in spatial frequency or orientation [3, 7, 8] Probability summation was also found across space for wavelet subband quantization distortions presented against a uniform background in [4]. Accordingly, probability summation is commonly assumed both for perceptual quantization schemes and for visualdistortion metrics [4, 9] HVS sensitivities to compound distortions induced by quantization of pairs of DWT subbands were recently measured by the authors [6] When compound distortions ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Tangand, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process., vol. 6, pp. 1164--1175, 1997.

....class to which it belongs. The threshold values used for I and P frames are shown in Table 6.1. Threshold value Threshold No. I frames P frames Th 40.0 6.0 Table 6.1: Thresholds values for I and P frames. The basic quant matrix ( BQM ) used for I frames is shown in the Table 6. 2 [36]. For P and B frames all the step sizes except the DC coefficient step size in the quant matrix are same. For only I and P frames this adaptive quantization is carried out and for B frames macroblock wise adaptation is not done as the bit budget for B frames is less. For B frames fixed step size ....

Andrew B. Watson, Gloria Y. Yang, Joshua A. Solomon, and John Villasenor, "Visibility of wavelet quantization noise", IEEE Trans. on Image Processing, pp. 1164- 1175, Aug. 1997.

....it is possible to determine the just noticeable distortion (JND) for each spatial frequency from specified wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [27] and wavelet [38]. Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [38] to determine the maximum capacity that is allowed for a watermark encoder. 1) Complementary Modulation: In what follows, a complementary modulation strategy will be presented. The ....

....wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [27] and wavelet [38] Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [38] to determine the maximum capacity that is allowed for a watermark encoder. 1) Complementary Modulation: In what follows, a complementary modulation strategy will be presented. The proposed scheme embeds two watermarks, which play complementary roles in resisting various kinds of attacks. The ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, 1997.

....of image visual quality. There has been substantial work in vision science that tries to understand and model the human visual system s behavior. It has been recognized that the visual sensitivity varies as a function of several key image dimensions, such as light level [2] spatial frequency [3][4], color [5] local image contrast [2] 6] eccentricity [7] and temporal frequency [8] The most common method of visually optimizing compression algorithms is to transform the amplitudes of the image to a perceptually uniform domain. Since the visual system s gray scale behavior is approximately ....

....4 shows some visual comparisons with some discussions. 2 Visual Frequency Weighting One common visual optimization strategy for compression is to make use of the contrast sensitivity function (CSF) that characterizes the varying sensitivity of the visual system to 2D spatial frequencies [3][4], as shown in Fig. 3. In general, human eyes are less sensitive to high frequency errors than to low frequency errors. The CSF can be used to determine the relative accuracies needed across differing spatial frequencies, where the term weight is used to describe the desired proportional ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Yang, J. Solomon and J. Vilasenor, "Visibility of wavelet quantization noise," IEEE Tran. Image Proc., vol. 6, No.8, pp. 1164-1175, 1997.

....account the properties of the human visual systems (HVS) in the optimization process. One common visual optimization strategy for compression is to make use of the contrast sensitivity function (CSF) that characterizes the varying sensitivity of the visual system to 2D spatial frequency [1] 2][3]. The advantage of this technique, however, becomes less noticeable for lower resolution display and closer viewing distance, since the CSF curve tends to be flat under those viewing conditions. Visual masking is a perceptual phenomenon where artifacts are locally masked by the image acting as a ....

Watson, Yang, Solomon and Vilasenor, "Visibility of wavelet quantization noise," IEEE Tran. Image Proc., vol. 6, No.8, pp. 1164-1175, 1997.

....locally invariant frequency weighting can be exploited. 2. VISUAL FREQUENCY WEIGHTING One common visual optimization strategy for compression is to make use of the contrast sensitivity function (CSF) that characterizes the varying sensitivity of the visual system to 2D spatial frequencies [4][5], as shown in Fig. 1. In general, human eyes are less sensitive to high frequency errors than to low frequency errors. The CSF can be used to determine the relative accuracies needed across differing spatial frequencies, where the term weight is used to describe the desired proportional accuracy. ....

Watson, Yang, Solomon and Vilasenor, "Visibility of wavelet quantization noise," IEEE Tran. Image Proc., vol. 6, No.8, pp. 1164-1175, 1997.

.... to be taken into account in order to achieve better subjective results [1] In transform based coding, the sensitivity of the human viewer to the transform basis functions should be taken into account to adapt the quantization step size for each coefficient to minimize the perceived distortion [2, 3]. As stated by Watson [ there are two ways to exploit the HVS characteristics in image coding: a) the usual signal based way, which consists of adapting the conventional approach based on minimizing the average error [4] through the appropriate perceptual distortion metric, and b) an ....

....is assumed to be valid for suprathreshold amplitudes (as is done in simple linear models) the amplitude dependent term in eq. 2 vanishes and the CSF based metric [26, 27] is obtained. If a given coding scheme uses some particular transform basis, specific incremental threshold data should be used [2, 3]. However, as the impulse responses of the perceptual filter bank, T , closely resemble the basis functions used in image coding transforms [28, 29] a similar behavior can be expected 2 . Therefore the metric W can be considered a reasonable approximation with any generic local frequency ....

A. Watson, G. Yang, J. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Transactions on Image Processing, vol. 6, pp. 1164-- 1175, 1997.

....is determined by the visual frequency of the transform coefficient, there will be one CSF weight per sub band in the wavelet transform. The design of the CSF weights is an encoder issue and depends on the specific viewing condition under which the decoded image is to be viewed. Please refer to [29][30] for more details of the design of the CSF weights. In many cases, only one set of CSF weights is chosen and applied according to the viewing condition. This application of visual frequency weighting is referred to as fixed visual weighting. In the case of embedded coders, as the coding bit ....

Watson, G. Yang, J. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. on Image Proc., vol. 6, pp. 1164-1175, 1997. K.6 Error resilience

....a quantization level q, a real value x can be quantized as x = j x q k Delta q r; where q is a quantization level and 0 r q is a quantization noise. To preserve the visual quality of watermarked image, the modifications of wavelet coefficients should not exceed the marking threshold [9]. Assume there are two watermark symbols, the quantization function is defined as: Q(x; q) Sk if j x q k mod 2 = k; where x is a real value, q is a quantization level and Sk ; k = 0; 1 are the watermark symbols. For binary watermark, the embedding rules are as follows. In case of target ....

Andrew B. Watson, Gloria Y. Yang, Joshua A. Solomon, and John Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. on Image Processing, vol. 6, no. 8, pp. 1164-- 1175, August 1997.

....method, a watermark value is encoded by modulating a selected wavelet coecient into a quantized interval. Basically, the quantity they used for modulation, which is monotonously increased from high resolution to low resolution, violates the capacity constraint of the human visual system [13]. They de ned a tamper assessment function (TAF) which is the ratio of the number of tampered coecients to the total number of coecients in a speci c subband, in order to measure the degree of tampering. They also point out if the TAF values decrease monotonously from high reso2 lution to low ....

....the probability of watermark error caused by an incidental distortion can be reduced by either enlarging the quantization interval or reducing the quantity of modi cations on coecients. However, it is well known that the maximum quantization interval should be bounded by the human visual system [13] so that visual quality can be maintained. As a consequence, the only methodology that we can adopt here is to increase the robustness by decreasing the variance of coecients. Owing to the fact that the variance of the sub block mean is smaller than that of an individual sample, we know that a ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, \Visibility of wavelet quantization noise," IEEE Trans. on Image Processing, vol. 6, pp. 1164-1175, August 1997.

....it is possible to determine the just noticeable distortion (JND) for each spatial frequency from specified wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [27] and wavelet [38]. Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [38] to determine the maximum capacity that is allowed for a watermark encoder. 2.3.1 Complementary Modulation In what follows, a complementary modulation strategy will be presented. ....

....wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [27] and wavelet [38] Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [38] to determine the maximum capacity that is allowed for a watermark encoder. 2.3.1 Complementary Modulation In what follows, a complementary modulation strategy will be presented. The proposed scheme embeds two watermarks, which play complementary roles in resisting various kinds of attacks. The ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of Wavelet Quantization Noise", IEEE Trans. Image Processing , Vol. 6, pp. 1164-1175, 1997.

....wavelet coders and reveals a significant perceptual improvementwhen images exhibit supra threshold distortion. 1. INTRODUCTION Previous work to develop perceptually based quantization strategies for wavelet coding has been geared towards providing visually lossless or sub threshold compression [1], 2] When compression artifacts become visible and the compression algorithm is operating in the supra threshold regime, the most common approach in the literature is to simply scale the quantization resulting from applying the perceptual model derived for sub threshold compression. This ....

....levels. 4. APPLICATION TO COMPRESSION 4.1. Intra band subband coding The proposed perceptual quantization strategy was used in a simple intra band subband coder, with run length and Huffman coding. Figure 1 shows sailboat compressed at 0. 2 bpp with the quantization step sizes given in [1], and with the proposed quantization strategy. The step sizes given in [1] were originally proposed for the sub threshold regime, and were multiplied by a constant to achieve the desired compression ratio. The images in Figure 1 show a significant perceptual improvement with the proposed ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise", IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1164-1175, August 1997.

....scale while under sensitivity may only happen at the middle to large scale. Under the circumstances, a user can make application dependent decisions about whether an image, which is JPEG compressed, still has credibility. However, their approach violates the nature of the human visual system [33]; thus, their system is confused when an image is JPEG compressed first and then maliciously tampered. Another disadvantage associated with Kundur and Hatzinakos s approach [13] is that their tampering detection results are very unstable. As we can see from their quantization process, the value of ....

....is required in the detection process. In the cocktail watermarking scheme [18, 19] there are three major ways to achieve robustness. They are: 1) bipolar watermarking (the designated watermark) 2) complementary modulation (the hiding rule) and (3) use of a wavelet based human visual system [33] to control the hiding strength. 5 Our theoretical analysis and experimental results have shown that cocktail watermarking can really achieve the requirement of high robustness. In cocktail watermarking [18, 19, 20] the complementary modulation rules used in the embedding process is summarized ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of Wavelet Quantization Noise", IEEE Trans. Image Processing , Vol. 6, pp. 1164-1175, 1997.

....it is possible to determine the just noticeable distortion (JND) for each spatial frequency from specified wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [21] and wavelet [31]. Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [31] to determine the maximum capacity that is allowed for a watermark encoder. 2.3.1 Complementary Modulation In what follows, a complementary modulation strategy will be presented. ....

....wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [21] and wavelet [31] Since wavelet transform is very powerful in image representation, we shall use the wavelet based visual model [31] to determine the maximum capacity that is allowed for a watermark encoder. 2.3.1 Complementary Modulation In what follows, a complementary modulation strategy will be presented. The proposed scheme embeds two watermarks, which play complementary roles in resisting various kinds of attacks. The ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of Wavelet Quantization Noise", IEEE Trans. Image Processing , Vol. 6, pp. 1164-1175, 1997.

....3D reactive quantum scattering and solution of 2D Navier Stokes equation with non periodic boundary conditions. The present work extends the DAF approach to image processing by constructing interpolating DAF wavelets [3] An earlier Group Normalization (GN) technique [4] and human vision response [5] are utilized to normalize the equivalent decomposition filters (EDFs) and perceptual luminance sensitivity. The combined DAF Visual Group Normalization (VGN) approaches achieve robust image restoration results. This work was supported by the National Science Foundation under Grant CHE 9700297, ....

....An image is a human vision dependent source. Using a just noticeable distortion profile, we can efficiently remove the visual redundancy as well as normalize the coefficients with respect to perception importance. A mathematical model for a perception lossless matrix Y m has been presented in [5] and is used as perceptual normalization combined with the EDF magnitude normalization. Note here that we use l m for magnitude normalization and not the wavelet basis function amplitude in [5] because the digital image decomposition is completely done using filter banks. We denote the ....

[Article contains additional citation context not shown here]

Andrew B. Watson, Gloria Y. Yang, Joshua A Solomon, and John Villasenor "Visibility of wavelet quantization noise," IEEE Transactions on Image Processing, Vol. 6, pp. 1164-1175, 1997.

....the size of the stimuli decreases) This fact of visual response is used to construct the perceptual normalization that enables efficient removal of the visual redundancy with respect to the perceptual importance. A simple nonlinear model of different frequency bands has been presented in [8], which can be used to construct the perceptual normalization response magnitude Y j,m in luminance spaces. We extend the definition as 2 0 2 log , 10 = R d f k m j m j a Y (14) where a defines the minimum threshold, k is a constant, R is the display visual resolution (DVR) f 0 is ....

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164-1175, 1997.

....in block (j,m) are normalized with a magnitude factor l j,m [3] 2) The visibility of coefficients depends on the display visual resolution. The just noticeable threshold is used to construct the perceptual normalization matrix Y j,m that enables efficient removal of the visual redundancy [4]. 3) Visual sensitivity is defined as the inverse of the contrast to produce a threshold response C j,m [5] The variations in sensitivity as a function of light level are primarily due to the light adaptive properties of the retina and are referred to as the amplitude nonlinearity of the human ....

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164-1175, 1997.

....correctly reflect the true strength of the various signal components. In order to achieve the best noise removing efficiency, the visual response is best accounted for by a perceptual normalization based on the property of the human vision system (HVS) The concept of visual loss less quantization [44] is employed to construct the visual loss less matrix, which re adjusts the magnitudenormalized coefficients. Perceptual signal processing has the potential of overcoming the limits of the traditional Shannon Ratedistortion (R D) theory for perception dependent information, such as images and ....

....environments. Using a just noticeable distortion profile, we can efficiently remove the visual redundancy from decomposition coefficients and normalize them with respect to a standard of perception importance. A practical, simple model for perception efficiency has been presented by Watson, et al. [44] for data compression. This model is adapted here to construct the perceptual lossless response magnitude Y j,m for normalizing according to the visual response function, 2 0 2 log , 10 = R d f k m j m a Y , 33) where a defines the minimum threshold, k is a constant, R is the ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164-1175, 1997.

....display resolution, it can determine the just noticeable distortion (JND) for each spatial frequency from specified wave functions. Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [19] and wavelet [37]. Since wavelet transform is very powerful in image representation, we will use the wavelet based frequency masking model [37] for watermarking. The frequency masking map with a four level wavelet transform and display visual resolution (DVR) 32 [37] is illustrated in Fig. 1. Whiter gray values ....

.... Psychologists have experimented with several contrast sensitivity functions (CSF) from some specific wave functions, such as the DCT basis function [19] and wavelet [37] Since wavelet transform is very powerful in image representation, we will use the wavelet based frequency masking model [37] for watermarking. The frequency masking map with a four level wavelet transform and display visual resolution (DVR) 32 [37] is illustrated in Fig. 1. Whiter gray values imply higher JND values. Two very popular watermarking techniques which employed perceptual significance were presented in [4, ....

[Article contains additional citation context not shown here]

A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of Wavelet Quantization Noise", IEEE Trans. Image Processing , Vol. 6, pp. 1164-1175, 1997.

....3 , which means that each image requires tens of megabytes of memory [1] During 90 s the use of spectral imaging has increased also in many fields of industry. Wavelets have been successfully used to compress binary images [2] 3] gray scale images [4] 5] and standard RGB color images [6] [7] but for multispectral images other methods have been used. Some of these are lossless [1] 8] 9] some near lossless [10] and many use lossy schemes [11] 12] 13] Highdimensional wavelets have been used to compress seismic data [14] This paper shows advantages of different wavelet ....

A. B. Watson, G. Y. Yang, J. A. Solomon and J. Villasenor, Visibility of Wavelet Quantization Noise, IEEE Transactions on Image Processing, 6(8), 1997, 1164-1175.

....features together because they are retained in the same detail signal. Diagonal details are retained in the detail signal from the next level of decomposition. It has been shown that the sensitivity of the HVS to quantization of horizontal and vertical wavelet coefficients is about the same [9, 10] so this is not a problem. 2 Wavelet Decomposition on the Quincunx Lattice Wavelet decomposition has two basic steps: filtering and subsampling. The input image is filtered by a lowpass and a high pass filter and both resulting signals are down sampled. The filtering process is accomplished by ....

Andrew B. Watson, Gloria Y. Yang, Joshua A. Solomon, John Villasenor "Visibility of Wavelet Quantization Noise." IEEE Trans. Image Processing Vol. 6, No. 8, August 1997.

....problem would involve a reliable mathematical model of human visual perception which unfortunately is not yet available. However, starting with the simplest model of an uniform scalar quantizer with an overall stepsize q 1 , we keep the option of a perceptual weighting of the quality factor q [13]. To absorb those wavelet coefficients, which are essentially related to noise, we have implemented a deadzone, i.e. a larger zero bin [ Gamma ; The ratio j of zero bin size to stepsize of j = 2 q = 1:5 (1) was found empirically to be a good choice for all tested image sources at various ....

A. B. Watson, G. Y. Yang, J. A. Solomon and J. Villasenor, "Visibility of Wavelet Quantization Noise", to appear in IEEE Trans. on IP, 1997.

....has been invested in understanding properties of the human visual system, in order to apply this knowledge in the development of solutions to image processing problems. Recently, visual models have been developed specifically for the performance evaluation of lossy image compression algorithms [8] (i.e. algorithms which degrade the original image quality in their reconstruction, in order to achieve higher compression ratios than would be otherwise possible) One common paradigm for perceptual coding is based on deriving an image dependent mask containing the just noticeable differences ....

A. Watson, G. Yang, J. Solomon, and J. Villasenor. Visibility of Wavelet Quantization Noise. IEEE Transactions on Image Processing, 6(8):1164--1175, August 1997.

....without resulting in any perceived distortion. This is usually referred to as the just noticeable distortion level or JND. We will look closely at the metrics developed by Safranek and Johnston for subband coders [5] by Watson for DCT coders [6] and by Watson et al. for wavelet based coders [12]. Most of the existing models for image quality and compression deal with the threshold of perception. In an increasing number of applications, however, there is a need to achieve very high compression ratios, and in such cases, a certain amount of perceived distortion is unavoidable. In ....

.... of the display device (in pixels per inch) Alternatively, one can specify the viewing distance in image heights and the image height in pixels (assuming the same horizontal and vertical display resolution) In either case, one must derive the display visual resolution in pixels per degree [12]. Since the contrast sensitivity function has a band pass characteristic (e.g. see [2] if we assume a single fixed viewing distance, the metric may show a degradation in image quality as we move away from the image. To avoid this, one can assume a range of viewing distances [2] or a minimum ....

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Proc., vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process., vol. 6, no. 8, pp. 1164--1175, Aug. 1997.

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A.B. Watson, G.Y. Yang, J.A. Solomon and J. Villasenor,"Visibility of wavelet quantization noise," IEEE Transactions on Image Processing, 6(8), 1164-1175 (1997).

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solmon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1164-1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1164-1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, no. 8, pp. 1164-1175, Aug. 1997.

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Watson, A., Yang, G., Solomon, J. and Villasenor, J. (1997):Visibility of wavelet quantization noise. IEEE Trans. on Image Processing, 6(8): 1164-1175.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Tangand, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process., vol. 6, pp. 1164--1175, 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Proc., vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Proc., vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164--1175, Aug. 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process. 6, pp. 1164--1175, 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Transactions on Image Processing 6, pp. 1164--1175, AUGUST 1997.

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A. B. Watson, G. Y. Tang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process., 6, pp. 1164-1175, 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor. Visibility of Wavelet Quantization Noise. IEEE Transactions on Image Processing, 6(8):1164-1175, August 1997.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Process. 6, 1164--1175 #1997#.

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A. B. Watson, G. Y. Yang, J. A. Solomon, and J. Villasenor, "Visibility of wavelet quantization noise," IEEE Trans. Image Processing, vol. 6, pp. 1164-1175, 1997.

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