JPEG2000图像编码的若干关键性技术研究
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摘要
随着信息技术的发展,3G移动通信技术渐渐推广,数字电视、高清家庭影院日益普及,数字电影逐渐取代传统的胶片电影,数码相机、数码摄像机等电子产品的性能迅速提高,图像和视频等视觉信息在人们的生产、生活中占有越来越重要的地位,人们对视觉信息的质量要求也越来越高,相应地也对图像/视频编码技术提出了越来越高的要求。JPEG2000/motion-JPEG2000编码标准适应当前对图像/视频编码技术的要求,逐渐成为流行标准。本文针对JPEG2000/motion-JPEG2000应用中相关的系列关键性技术做了研究,主要内容如下。
首先本文对JPEG2000 ROI编码技术做了研究。JPEG2000中定义了两种ROI编码方法:MaxShift方法和General Scaling Based(GSB)方法。在低码率应用环境下,MaxShift方法有可能把所有背景信息全部丢弃,但是有些应用中需要一定的背景信息;GSB方法虽然在一定程度上弥补了MaxShift方法的不足,但是需要形状编码。由于形状编码的复杂性,JPEG2000只规定了矩形和椭圆两种形状,而这两种形状不能精确地描述任意形状的ROI,导致编码效率降低。因此,高效地编码任意形状的ROI和在低码率环境下保持一定背景信息成为JPEG2000 ROI编码的研究重点。由于在总码率受限的情况下提高背景质量和提高ROI质量相矛盾,有学者提出了折衷的解决方法:控制ROI和背景的相对质量。现有的控制相对质量的方法是通过控制ROI和背景的相对码率实现的,这类实现方法主要有以下三个缺点:①相对码率计算复杂,②只有完全解码后才能实现预定的相对质量,③以不受限制码率解码时,图像背景区质量低。高效编码任意形状ROI的方法之一是对位平面重排,使得解码器能够根据位平面位置区分ROI和背景比特,或者不需要区分ROI和背景就能解码,从而不需要编码端提供ROI形状信息。针对控制相对码率方法的第一个缺点,本文提出了通过控制参与解码的ROI和背景位平面数量相对值来控制其相对质量的思路。然后基于控制两类位平面相对数量和位平面重排的思想,本文提出了两种ROI编码方法,一种是适用于常见较小深度值图像的位平面段移动(BPSShift)方法,一种是适用于较大深度图像的位平面组移动(BPGShift)方法。编码时BPSShift方法首先对ROI和背景位平面进行分段;然后以位平面段为单位,从权重较大的部分开始对ROI和背景位平面进行移动重排,使得ROI位平面段和背景位平面段间隔排列。由于两类位平面段的数量可能不相同,当数目少的一类位平面段排列完后,另一类位平面段的剩余部分全部排列到低权重的位平面位置。当图像以中低码率解码时,随着码率的提高,参与解码的ROI和背景位平面数量以大致恒定的比例增加,这个数量比约等于两类位平面段大小之比。相应地,解码图像保持大致恒定的相对质量。因此两类位平面段大小之比可以作为两部分图像相对质量的近似度量。由于BPSShift方法可以不丢弃任何位平面,所以当解码码率不受限制时,解码图像的ROI区和背景区能够都有很高的质量。由于ROI位平面段和背景位平面段处于不同的位平面位置,解码器能够根据其位置的不同对它们进行区分,所以BPSShift方法能够解码任意形状的ROI而不需要编码端提供任何形状信息。当使用BPSShift方法对较大深度图像编码时有可能使用大位平面段,大位平面段可能导致解码图像的相对质量变动较大,针对这个问题本文提出了BPGShift方法加以解决。BPGShift方法在BPSShift方法的基础上把位平面段进一步划分成子段,并增加了细化位平面排列的子段排列运算,使得在大位平面段情况下解码图像的相对质量更加稳定。BPSShift方法和BPGShift方法的主要运算都是移动位平面,因此实现简单,计算量小。此外这两种方法的附加数据量小,都支持多ROI图像的编码。
然后本文对motion-JPEG2000错误隐藏技术做了研究。由于沿高频方向相邻小波系数之间相关性极弱,沿低频方向的相关性随系数间的距离增大衰减很快,所以使用空间邻近系数信息的错误隐藏方法对高频子带大尺寸误码块的错误隐藏效果并不理想。由于离散小波变换的移变性,所以不能直接使用运动补偿方法从相邻帧的信息中恢复高频子带误码块。为了解决移变性问题,本文引入了cycle-spinning算法,利用cycle-spinning把移变系数转变成移不变的系数。在此基础上,本文提出了基于cycle-spinning的错误隐藏方法。该方法首先利用cycle-spinning算法把参考帧中具有移变性的高频子带系数转变成移不变系数,然后使用运动补偿从移不变的相邻帧系数中得到误码块应有的信息,恢复误码块,达到隐藏错误的目的。基于cycle-spinning的错误隐藏方法可以用于各个高频子带大尺寸编码块的错误隐藏,包括通常错误隐藏方法不适用的HH子带。
最后本文以JPEG2000熵编码框架为基础,对超完备小波图像编码进行了研究。常用小波(包括JPEG2000中定义的小波)的局限性,使得冗余字典图像稀疏编码方法成为研究热点之一,然而如何选择最小的子字典成为冗余字典稀疏编码方法中一个待解决的问题。由于超完备小波集可以看作冗余字典,小波分解系数是图像在小波上的投影,所以对超完备小波分解系数的选择就是对子字典的选择。本文把聚类、模式识别领域的mean shift方法引入到超完备log-Gabor小波分解系数的选择算法中,对Fischer等人的超完备小波系数选择方法进行改进,提出了基于mean shift的超完备log-Gabor小波分解系数选择方法,取得了比Fischer等人的方法更快的选择速度。然后在本文提出的系数选择方法基础上,借用JPEG2000中的熵编码方法构建了稀疏编码方案。实验证明在产生相近PSNR解码图像的情况下,本文所构造的稀疏编码方法虽然压缩率稍低于JPEG2000有损压缩,但它明显的减少了解码图像的artifact,具有更好的主观图像质量。因此基于mean shift的log-Gabor小波系数选择方法能够有效地选择系数,适合用于超完备log-Gabor小波图像稀疏编码;本文提出的稀疏编码方案有一定优点,值得进一步研究完善。
With the development of information technology, the usage of the third genera-tion mobile communication is spreading, digital TV and high-definition home theater are being popularized, traditional film is replaced by digital cinema gradually, and digital camera and digital vidicon become powerful increasingly, resulting that visual information plays more and more important role in people's life and work, and people want visual information with better quality. Accordingly, the image/video coding technique becomes more sophisticated. JPEG2000/motion-JPEG2000 becomes pre-dominant standards gradually for image/video coding. Some key techniques about JPEG2000/motion-JPEG2000 are studied in this dissertation, and the achievements in this dissertation are described in what follows.
For JPEG2000 Region-Of-Interset (ROI) coding, there are two ROI coding method in JPEG2000 standard: the maxshift method and the General Scaling Based method (GSB). The MaxShift method can discards all of the background information for the low bit rate cases. The GSB method overcomes the maxshift method’s short-coming to some extent, but it need shape coding. Considering about the computational complexity of shape coding, JPEG2000 standard only defines two kinds of shapes, i.e. rectangle and ellipse. However those shapes cannot describe arbitrary shaped ROI precisely. Thus, keeping a portion of background information in low bit rate case and coding arbitrarily shaped ROI efficiently become the hotspots of research. Improving BackGound (BG) quality is contradicted with improving ROI quality in the limited bit rate cases, and the tradeoff is controlling the relative quality between ROI and BG. The idea of dealing with bit planes in section is proposed in this dissertation, as well as a new measurement of the relative quality between ROI and background. The crite-rion of measure is the size ratio between the ROI section and the background section, while the existed measurement is the bit rate ratio between the ROI and the BG area with large computational cost. There are two novel ROI coding methods, Bit Plane Section Shift (BPSShift) method and Bit Plane Group Shift (BPGShift)method, are designed based on the above new idea and measurement. The images decoded in dif-ferent bit rate by BPSShift method have relatively constant relative quality, i.e. BPSShift method keeping sufficient background information. The main operation in BPSShift method is shifting, so the BPSShift method has low computational cost. The ROI bits and background bits can be identified from their positions in bit planes, so BPSShift method can code arbitrary ROI without shape coding. When the BPSShift is applied to coding a large deepth image, the section may be large, which lead to the decoded images may have unstable relative quality. The BPGShift method resolves this problem. The BPGShift method is an enhanced method of BPSShift method, which devides each bit plane section into three subsections, and rearranges the sub-sections after the bit planes are shift in sections.
Then, error concealment for motion-JPEG2000 is researched. For the adjacent coefficients along the high frequency direction have week relation, and the relation between two coefficients along the low frequency direction decreasing rapidly ac-cording to the distance, the interpolation based error concealment methods are ineffi-cient for large code blocks in high frequency subbands. Motion compensation method is inefficient for high frequency subbands error concealment because the translation variant character of DWT. The cycle-spinning algorithm is introduced into error con-cealment in this dissertation. The high frequency coefficients become translation in-variant after being processed with the cycle-spinning algorithm. Then the translation invariant coefficients are used to conceal the error by motion compensation method. The proposed error concealment method can be used in large error block cases of all kinds of high frequency subband including the HH subband.
In the end, researches are done on overcomplete wavelet image coding based on the scheme of JPEG2000 entropy coding. Sparse image coding with redundant dic-tionary becomes a hotspot for the limitation of popular wavelets. Nevertheless, how to minimize the size of the subdictionary is still the unsolved problem. A wavelet coeffi-cient is the projection of the image on a wavelet, and the set of overcomplete wavelets can be regarded as an overcomplete dictionary. Therefore coefficient selection is equivalent to subdictionary selection. The mean shift algorithm is introduced into overcomplete log-Gabor wavelet coefficient selection from the clustering and pattern recognition domain. An improved coefficient selection method is proposed based on the mean shift algorithm, which converges faster than the prototype. To test the per-formance of the proposed coefficient selection method, a compression scheme is de-signed based on the proposed coefficient selection method and JPEG2000 entropy coding algorithm. The experiments show that the proposed method can select the co-efficents effectively. The reconstructed images represented by the selected coefficients appear more pleasant to the human eyes than those decoded with JPEG2000.
首先本文对JPEG2000 ROI编码技术做了研究。JPEG2000中定义了两种ROI编码方法:MaxShift方法和General Scaling Based(GSB)方法。在低码率应用环境下,MaxShift方法有可能把所有背景信息全部丢弃,但是有些应用中需要一定的背景信息;GSB方法虽然在一定程度上弥补了MaxShift方法的不足,但是需要形状编码。由于形状编码的复杂性,JPEG2000只规定了矩形和椭圆两种形状,而这两种形状不能精确地描述任意形状的ROI,导致编码效率降低。因此,高效地编码任意形状的ROI和在低码率环境下保持一定背景信息成为JPEG2000 ROI编码的研究重点。由于在总码率受限的情况下提高背景质量和提高ROI质量相矛盾,有学者提出了折衷的解决方法:控制ROI和背景的相对质量。现有的控制相对质量的方法是通过控制ROI和背景的相对码率实现的,这类实现方法主要有以下三个缺点:①相对码率计算复杂,②只有完全解码后才能实现预定的相对质量,③以不受限制码率解码时,图像背景区质量低。高效编码任意形状ROI的方法之一是对位平面重排,使得解码器能够根据位平面位置区分ROI和背景比特,或者不需要区分ROI和背景就能解码,从而不需要编码端提供ROI形状信息。针对控制相对码率方法的第一个缺点,本文提出了通过控制参与解码的ROI和背景位平面数量相对值来控制其相对质量的思路。然后基于控制两类位平面相对数量和位平面重排的思想,本文提出了两种ROI编码方法,一种是适用于常见较小深度值图像的位平面段移动(BPSShift)方法,一种是适用于较大深度图像的位平面组移动(BPGShift)方法。编码时BPSShift方法首先对ROI和背景位平面进行分段;然后以位平面段为单位,从权重较大的部分开始对ROI和背景位平面进行移动重排,使得ROI位平面段和背景位平面段间隔排列。由于两类位平面段的数量可能不相同,当数目少的一类位平面段排列完后,另一类位平面段的剩余部分全部排列到低权重的位平面位置。当图像以中低码率解码时,随着码率的提高,参与解码的ROI和背景位平面数量以大致恒定的比例增加,这个数量比约等于两类位平面段大小之比。相应地,解码图像保持大致恒定的相对质量。因此两类位平面段大小之比可以作为两部分图像相对质量的近似度量。由于BPSShift方法可以不丢弃任何位平面,所以当解码码率不受限制时,解码图像的ROI区和背景区能够都有很高的质量。由于ROI位平面段和背景位平面段处于不同的位平面位置,解码器能够根据其位置的不同对它们进行区分,所以BPSShift方法能够解码任意形状的ROI而不需要编码端提供任何形状信息。当使用BPSShift方法对较大深度图像编码时有可能使用大位平面段,大位平面段可能导致解码图像的相对质量变动较大,针对这个问题本文提出了BPGShift方法加以解决。BPGShift方法在BPSShift方法的基础上把位平面段进一步划分成子段,并增加了细化位平面排列的子段排列运算,使得在大位平面段情况下解码图像的相对质量更加稳定。BPSShift方法和BPGShift方法的主要运算都是移动位平面,因此实现简单,计算量小。此外这两种方法的附加数据量小,都支持多ROI图像的编码。
然后本文对motion-JPEG2000错误隐藏技术做了研究。由于沿高频方向相邻小波系数之间相关性极弱,沿低频方向的相关性随系数间的距离增大衰减很快,所以使用空间邻近系数信息的错误隐藏方法对高频子带大尺寸误码块的错误隐藏效果并不理想。由于离散小波变换的移变性,所以不能直接使用运动补偿方法从相邻帧的信息中恢复高频子带误码块。为了解决移变性问题,本文引入了cycle-spinning算法,利用cycle-spinning把移变系数转变成移不变的系数。在此基础上,本文提出了基于cycle-spinning的错误隐藏方法。该方法首先利用cycle-spinning算法把参考帧中具有移变性的高频子带系数转变成移不变系数,然后使用运动补偿从移不变的相邻帧系数中得到误码块应有的信息,恢复误码块,达到隐藏错误的目的。基于cycle-spinning的错误隐藏方法可以用于各个高频子带大尺寸编码块的错误隐藏,包括通常错误隐藏方法不适用的HH子带。
最后本文以JPEG2000熵编码框架为基础,对超完备小波图像编码进行了研究。常用小波(包括JPEG2000中定义的小波)的局限性,使得冗余字典图像稀疏编码方法成为研究热点之一,然而如何选择最小的子字典成为冗余字典稀疏编码方法中一个待解决的问题。由于超完备小波集可以看作冗余字典,小波分解系数是图像在小波上的投影,所以对超完备小波分解系数的选择就是对子字典的选择。本文把聚类、模式识别领域的mean shift方法引入到超完备log-Gabor小波分解系数的选择算法中,对Fischer等人的超完备小波系数选择方法进行改进,提出了基于mean shift的超完备log-Gabor小波分解系数选择方法,取得了比Fischer等人的方法更快的选择速度。然后在本文提出的系数选择方法基础上,借用JPEG2000中的熵编码方法构建了稀疏编码方案。实验证明在产生相近PSNR解码图像的情况下,本文所构造的稀疏编码方法虽然压缩率稍低于JPEG2000有损压缩,但它明显的减少了解码图像的artifact,具有更好的主观图像质量。因此基于mean shift的log-Gabor小波系数选择方法能够有效地选择系数,适合用于超完备log-Gabor小波图像稀疏编码;本文提出的稀疏编码方案有一定优点,值得进一步研究完善。
With the development of information technology, the usage of the third genera-tion mobile communication is spreading, digital TV and high-definition home theater are being popularized, traditional film is replaced by digital cinema gradually, and digital camera and digital vidicon become powerful increasingly, resulting that visual information plays more and more important role in people's life and work, and people want visual information with better quality. Accordingly, the image/video coding technique becomes more sophisticated. JPEG2000/motion-JPEG2000 becomes pre-dominant standards gradually for image/video coding. Some key techniques about JPEG2000/motion-JPEG2000 are studied in this dissertation, and the achievements in this dissertation are described in what follows.
For JPEG2000 Region-Of-Interset (ROI) coding, there are two ROI coding method in JPEG2000 standard: the maxshift method and the General Scaling Based method (GSB). The MaxShift method can discards all of the background information for the low bit rate cases. The GSB method overcomes the maxshift method’s short-coming to some extent, but it need shape coding. Considering about the computational complexity of shape coding, JPEG2000 standard only defines two kinds of shapes, i.e. rectangle and ellipse. However those shapes cannot describe arbitrary shaped ROI precisely. Thus, keeping a portion of background information in low bit rate case and coding arbitrarily shaped ROI efficiently become the hotspots of research. Improving BackGound (BG) quality is contradicted with improving ROI quality in the limited bit rate cases, and the tradeoff is controlling the relative quality between ROI and BG. The idea of dealing with bit planes in section is proposed in this dissertation, as well as a new measurement of the relative quality between ROI and background. The crite-rion of measure is the size ratio between the ROI section and the background section, while the existed measurement is the bit rate ratio between the ROI and the BG area with large computational cost. There are two novel ROI coding methods, Bit Plane Section Shift (BPSShift) method and Bit Plane Group Shift (BPGShift)method, are designed based on the above new idea and measurement. The images decoded in dif-ferent bit rate by BPSShift method have relatively constant relative quality, i.e. BPSShift method keeping sufficient background information. The main operation in BPSShift method is shifting, so the BPSShift method has low computational cost. The ROI bits and background bits can be identified from their positions in bit planes, so BPSShift method can code arbitrary ROI without shape coding. When the BPSShift is applied to coding a large deepth image, the section may be large, which lead to the decoded images may have unstable relative quality. The BPGShift method resolves this problem. The BPGShift method is an enhanced method of BPSShift method, which devides each bit plane section into three subsections, and rearranges the sub-sections after the bit planes are shift in sections.
Then, error concealment for motion-JPEG2000 is researched. For the adjacent coefficients along the high frequency direction have week relation, and the relation between two coefficients along the low frequency direction decreasing rapidly ac-cording to the distance, the interpolation based error concealment methods are ineffi-cient for large code blocks in high frequency subbands. Motion compensation method is inefficient for high frequency subbands error concealment because the translation variant character of DWT. The cycle-spinning algorithm is introduced into error con-cealment in this dissertation. The high frequency coefficients become translation in-variant after being processed with the cycle-spinning algorithm. Then the translation invariant coefficients are used to conceal the error by motion compensation method. The proposed error concealment method can be used in large error block cases of all kinds of high frequency subband including the HH subband.
In the end, researches are done on overcomplete wavelet image coding based on the scheme of JPEG2000 entropy coding. Sparse image coding with redundant dic-tionary becomes a hotspot for the limitation of popular wavelets. Nevertheless, how to minimize the size of the subdictionary is still the unsolved problem. A wavelet coeffi-cient is the projection of the image on a wavelet, and the set of overcomplete wavelets can be regarded as an overcomplete dictionary. Therefore coefficient selection is equivalent to subdictionary selection. The mean shift algorithm is introduced into overcomplete log-Gabor wavelet coefficient selection from the clustering and pattern recognition domain. An improved coefficient selection method is proposed based on the mean shift algorithm, which converges faster than the prototype. To test the per-formance of the proposed coefficient selection method, a compression scheme is de-signed based on the proposed coefficient selection method and JPEG2000 entropy coding algorithm. The experiments show that the proposed method can select the co-efficents effectively. The reconstructed images represented by the selected coefficients appear more pleasant to the human eyes than those decoded with JPEG2000.
引文
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[24] Wang Z., Bovik A.. “Bitplane-by-Bitplane Shift (BbBShift) — A suggestion for JPEG2000 Region Of Interest image coding”, IEEE Signal Processing Letters, Vol. 9, No. 5, pp 160-162, 2002.
[25] Liu L., Fan G.. “A new JPEG2000 region-of-interest image coding method: partial significant bitplanes shift”, IEEE Signal Processing Letter, Vol. 10, No. 2, pp 35-38, 2003
[1] ISO/IEC 15444-1, JPEG2000, Part 1, Mar., 2000..
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[3] ISO/IEC 15444-2, JPEG2000, Part 2, Mar., 2000
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[6] Wang Z., Bovik A.. “Bitplane-by-Bitplane Shift (BbBShift) — A suggestion for JPEG2000 Region Of Interest image coding”, IEEE Signal Processing Letters, Vol. 9, No. 5, pp 160-162, 2002.
[7] Liu L., Fan G.. “A new JPEG2000 region-of-interest image coding method: partial significant bitplanes shift”, IEEE Signal Processing Letter, Vol. 10, No. 2, pp 35-38, 2003.
[8] Subedar M., Karam L. and Abousleman G.. “An embedded scaling-based ar-bitrary shape region-of-interest coding method for JPEG2000”, IEEE Inter-national Conference on Acoustics, Speech, and Signal Processing, Vol. 3, pp 681-684, 2004.
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[16] http://www.jpeg.org/jpeg2000/CDs15444.html.
[1] ISO/IEC 15444-3, JPEG2000, Part 3, Mar., 2001.
[2] ISO/IEC 15444-1, JPEG2000, Part 1, Mar., 2000.
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[5] ISO/IEC 15444-1, JPEG2000, Part 1, Mar., 2000.
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[15] Candès E. and Donoho D.. “Curvelets - a surprisingly effective nonadaptive representation for objects with edges”, http://citeseer.ist.psu.edu/299305.html, 1999.
[16] Fischer S., Cristóbal G. and Redondo R.. “Sparse overcomplete Gabor wave-let representation based on local competitions”. IEEE Transactions On Im-age Processing, Vol. 15, No. 2, pp 265-272, 2006.
[17] Jiang Y., Zhong Z. and Wang L.. “A wavelet coding preprocessing algorithm based on Bayesian estimation for image compression”. Proceedings of theFourth International Conference on Machine Learning and Cybernetics, Vol. 9, pp 5467-5472, 2005.
[18] Pennec E., Mallat S.. “Sparse geometric image representations with bande-lets”. IEEE Transactions On Image Processing, Vol. 14, No. 4, pp 423-438, 2005.
[19] Wakin M., Romberg J., Choi H., etc. “Wavelet-Domain Approximation and Compression of Piecewise Smooth Images”. IEEE Transactions On Image Processing, Vol. 15, No. 5, pp 1071-1087, 2006.
[20] Marpe D., George V., Cycon H, etc. “Performance evaluation of Mo-tion-JPEG2000 in comparison with H.264/AVC operated in pure intra coding mode”, Proceedings of SPIE, Vol. 5266, pp 129-137, 2004.
[21] 陈彬,魏丹,陈勇。“H.264 帧内编码与 JPEG2000 的性能比较与分析”,计算机工程与科学,Vol.27,No. 12,pp48-50,2005.
[22] Yu W., Qiu R. and Fritts J.. “Evaluation of motion-JPEG2000 for video processing”, http://citeseer.ist.psu.edu/yu01evaluation.html, 2001.
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[25] Liu L., Fan G.. “A new JPEG2000 region-of-interest image coding method: partial significant bitplanes shift”, IEEE Signal Processing Letter, Vol. 10, No. 2, pp 35-38, 2003
[1] ISO/IEC 15444-1, JPEG2000, Part 1, Mar., 2000..
[2] Christopoulos C., Skodras A., Ebrahimi T.. “The JPEG2000 still image cod-ing system: an overview”, IEEE Transactions on Consumer Electronics, Vol. 46, No. 4, pp 1103-1127, 2000.
[3] ISO/IEC 15444-2, JPEG2000, Part 2, Mar., 2000
[4] Fukuma S., Ito M., Imajo C., etc. “A relative quality controlled re-gion-of-interest image coding based on wavelet transform”, The 45th IEEE Intl. Midwest Symposium on Circuits and Systems, Vol. 1, pp 459-462, 2002.
[5] Sanchez V., Basu A., Mandal M.. “Prioritized region of interest coding in JPEG2000”, IEEE Transactions on Circuits and Systems for Video Tech-nology, Vol. 14, No. 9, pp 1149-1155, 2004.
[6] Wang Z., Bovik A.. “Bitplane-by-Bitplane Shift (BbBShift) — A suggestion for JPEG2000 Region Of Interest image coding”, IEEE Signal Processing Letters, Vol. 9, No. 5, pp 160-162, 2002.
[7] Liu L., Fan G.. “A new JPEG2000 region-of-interest image coding method: partial significant bitplanes shift”, IEEE Signal Processing Letter, Vol. 10, No. 2, pp 35-38, 2003.
[8] Subedar M., Karam L. and Abousleman G.. “An embedded scaling-based ar-bitrary shape region-of-interest coding method for JPEG2000”, IEEE Inter-national Conference on Acoustics, Speech, and Signal Processing, Vol. 3, pp 681-684, 2004.
[9] Egger O., Fleury P. and Ebrahimi T.. “Shape-adaptive wavelet transform for zerotree coding”, Proceedings of Europe Workshop Image Analysis and Coding for TV, HDTV and Multimedia Application, Vol. 10, No.5, pp 201–208, 1996.
[10] Gilge M., Engelhardt T. and Mehlan R.. “Coding of arbitrarily shaped image segments based on a generalized orthogonal transform”, Signal Processing: Image Communication, Vol. 1, pp 153–180, 1989.
[11] Chang S. and Messerschmitt D.. “Transform coding of arbitrarily shaped image segments”, Proceedings of the first ACM international conference on Multimedia, pp 83–90, 1993.
[12] Li S., Li W., Ling F., etc. “Shape adaptive vector wavelet coding of arbitrarily shaped texture”, ISO/IEC JTC/SC29/WG11, MPEG-96-m1027, 1996.
[13] Li S. and Li W.. “Shape-adaptive discrete wavelet transforms for arbitrarily shaped visual object coding”, IEEE Transactions on Circuits and Systems For Video Technology, Vol. 10, No. 5, pp 725-743, 2000.
[14] Tian Y., Kong X.. “An improved shape-based arbitrary shape ROI coding method with SA-DWT in JPEG2000”, IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 2, pp 373-376, 2005.
[15] Cuhadar A. and Tasdoken S.. “Multiple, arbitrary shape ROI coding with ze-rotree based wavelet coders”, IEEE International. Conference. on Multi-media and Expo, Vol. 3, pp 257-267, 2003.
[16] http://www.jpeg.org/jpeg2000/CDs15444.html.
[1] ISO/IEC 15444-3, JPEG2000, Part 3, Mar., 2001.
[2] ISO/IEC 15444-1, JPEG2000, Part 1, Mar., 2000.
[3] ISO/IEC 15444-2, JPEG2000, Part 2, Mar., 2000.
[4] ISO/IEC JTC1/SC29/WG1 N2412. "The JPEG-2000 Still Image Compression Standard". 2005.
[5] Crouse M., Nowak R., and Baraniuk R.. “Wavelet-based statistical signal proc-essing using hidden Markovmodels”, IEEE Transactions On Signal Processing, Vol. 46, No. 4, April, pp 886-902, 1998.
[6] Coifman R., Donoho D.. “Translation-invariant de-noising”, Lect. Nots Stat., pp 125-150, 1995.
[7] 梁栋,沈敏,高清维等。 “一种基于 Contourlet 递归 Cycle Spinning 的图像去噪方法”,电子学报,Vol. 33,No. 11, pp 2044-2046, 2005。
[8] Nosratinia A.. “Postprocessing of JPEG-2000 images to remove compression ar-tifacts”, IEEE Signal Processing Letters, Vol. 10, No. 10, pp 296-299, 2003
[9] Zhao S., Han H., and Peng S.. “Wavelet-domain HMT-based image sup-per-resolution”, IEEE International Conference on Image Processing, Vol. 2, pp 933-936, 2003.
[10] Fletcher A., Ramchandran K.. “Wavelet denoising by recursive cycle spinning”, IEEE International Conference on Image Processing, Vol. 2, pp 873-876, 2002.
[11] Fletcher A., Goyal V. and Ramchandran K.. “Iterative projective wavelet methods for denoising”, Proceedings of SPIE, Vol. 5207, pp 9-15, 2003.
[12] Temizel A., Vlachos T.. “Wavelet domain image resolution enhancement using cycle-spinning”, Electronics Letters, Vol. 41, No. 3, pp 119-120, 2005.
[13] Temizel A., Vlachos T.. “Image resolution upscaling in the wavelet domain us-ing directional cycle spinning”, Journal of Electronic Imaging, Vol. 14, No. 4, pp 040501~1 – 040501~3, 2005.
[14] Azimifar Z., Fieguth P. and Jernigan E.. "Modeling the correlation structure of images in the wavelet domain", Canadian Conference on Electrical and Com-puter Engineering, Vol.2, pp 1123-1127, 2001.
[15] Rane S., Remus J. and Sapiro G.. "Wavelet-domain reconstruction of lost blocks in wireless image transmission and packet-switched networks", Interna-tional Conference on Image Processing, Vol.1, pp 309-312, 2002.
[16] http://www.seas.gwu.edu/~ayoussef/cs225/vectorquantization.html
[17] L. Atzori, G. Ginesu, A. Raccis and D.D. Giusto. A novel iterative approach for JPEG2000 error concealment, IEEE 6th Workshop on Multimedia Signal Proc-essing, pp 283-286, 2004.
[18] Lee P., Chen M., and Chen L.. “Error concealment algorithm using interested direction for JPEG2000 image transmission”, IEEE Transactions on Consumer Electronics, Vol.49, Issue 4, pp 1395-1401, 2003.
[19] Atzori L., Giusto D. and Raccis A.. "High-frequency error concealment in wave-let-based image coding", Electronics Letters, Vol.39, No.2, Jan. 2003.
[20] Linde Y., Buzo A., Gray R.. “An algorithm for vector quantizer design”, IEEE Transactions on Communications, Vol. Com-28, No.1, pp 84-95, 1980.
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