A smoothness constraint set based on local statistics of BDCT coefficients for image postprocessing
Introduction
The block-based discrete cosine transform (BDCT) [1] has been used widely in image and video compression. To reduce the bit-rate, the coefficients of BDCT are often quantized. At low bit rate, this causes annoying blocking artifacts in the decoded image. Recently, several postprocessing methods have been proposed to alleviate blocking artifacts. Postprocessing techniques are attractive because they are independent of coding schemes and can be applied to commonly used JPEG [1], H.263, and MPEG compression standards.
The approach based on the theory of POCS has a major advantage in that it can exploit the a priori knowledge about the image. If the convex constraints sets associated with the image information can be found, the POCS algorithm with corresponding projectors will converge to the intersection of all the constraint sets. In the past, various constraint sets have been proposed. Generally, these constraint sets can be classified into two categories. One is the quantization constraint set (QCS) [2], [3], and the other is the smoothness constraint set (SCS) [4], [5]. However, most SCS are implemented in the image domain, whereas QCS are defined in the BDCT domain. Therefore, a BDCT transform of the whole image is needed in each iteration. This incurs high computational cost. Although there are some filtering methods available that work in BDCT domain [6], they are not POCS-based and it is difficult to incorporate new a priori knowledge.
In this paper, we proposed a new SCS, which is defined in the BDCT domain. The new SCS is derived from signal and quantization noise statistics and uses a least mean square formulation based on the Wiener filter. Experiments show that POCS using this SCS not only has faster convergence but also has better objective and subjective performance. Moreover, this new SCS can be used as a new constraint set to improve most of the available POCS-based image postprocessing algorithms.
Section snippets
POC-based image reconstruction
In POCS-based image post-processing [7], every known a priori property about the original image can be formulated as a corresponding convex set in a Hilbert space H. Given n closed convex set Ci, i=1,2,…,n, and nonempty, the iterationwhere Pi is the projector onto Ci defined byand g is the projection of x onto Ci, will converge to a point in C0 for any initial x0.
The mathematical model of image deblocking problem
Throughout this paper we use the following conventions: a real N×N image
Proposed postprocessing technique
It is well known that the least mean square error solution for Eq. (5) is Wiener filtering. Specifically, the locally adaptive Wiener filter [8], which is capable of tracking the signal and noise characteristics over different image regions, can be used to estimate the true BDCT coefficients bywhere is the a prior mean of X, X, and Y are treated as an N2×1 vector in the space by lexicographic ordering by either rows or columns of their 2D versions. By
Spatially-adaptive algorithm based on human visual system
By far, our constraint set is only based on least square error measure, without considering the visual characteristic. In order to improve the visual quality of this method, we modified Eqs. (20), (21) to incorporate the property of human visual system (HVS) [13]. Due to the masking effect in the HVS, artifacts are more visible in smooth areas than in non-regular areas. In order to account for the masking effect, a block based classification method is necessary. Since our algorithm is
Perfoemance evaluation
We present some experimental results to evaluate the performance of the proposed recovery algorithm. A number of de facto standard 256 gray-level test images of size 512×512 are used. The decoded images, with visible blocking artifacts are obtained by JPEG compression with the quantization tables shown in Appendix.
For comparative studies, several popular deblocking algorithms reported in the literature, namely, (a) Rosenholtz's algorithm [9], (b) Yang's algorithm [4], (c) Paek's algorithm [5]
Conclusions
In this paper, a POCS-based deblocking algorithm utilizing a new smoothness constraint set is proposed. The new smoothness constraint set is constructed based on the local statistics of the BDCT transform coefficients and the probability density function (pdf) of the quantizer. The proposed method has been shown to give superior performance in comparison to several well-known POCS-based deblocking algorithms. Since no BDCT transform is needed in each POCS iteration, it has a low computational
Acknowledgements
This work is supported by a strategic research grant from City University of Hong Kong (Project 7001556).
Xiangchao Gan received his MS in Electrical and Electronic Engineering from Xi'an Jiaotong University, China, in 2001. He is currently studying for his PhD degrees at City University of HongKong. His research interests include image reconstruction, image compression and multimedia communication.
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Xiangchao Gan received his MS in Electrical and Electronic Engineering from Xi'an Jiaotong University, China, in 2001. He is currently studying for his PhD degrees at City University of HongKong. His research interests include image reconstruction, image compression and multimedia communication.
Alan Wee-Chung Liew received his BE with first class honors in Electrical and Electronic Engineering from the University of Auckland, New Zealand, in 1993 and PhD in Electronic Engineering from the University of Tasmania, Australia, in 1997. He is currently an Assistant Professor in the Department of Computer Science and Engineering, The Chinese University of Hong Kong. His current research interests include computer vision, medical imaging, pattern recognition and bioinformatics. He has served as a technical reviewer for a number of international conferences and journals in IEEE Transactions, IEE proceedings, bioinformatics and computational biology. Dr Liew is a member of the Institute of Electrical and Electronic Engineers (IEEE), and his biography is listed in the 2005 Marquis Who's Who in the World and Marquis Who's Who in Science and Engineering.
Hong Yan received a BE degree from Nanking Institute of Posts and Telecommunications, Nanking, China, in 1982, an MSE degree from the University of Michigan in 1984, and a PhD degree from Yale University in 1989, all in electrical engineering. In 1982 and 1983 he worked on signal detection and estimation as a graduate student and research assistant at Tsinghua University, Beijing, China. From 1986 to 1989 he was a research scientist at General Network Corporation, New Haven, CT, USA, where he worked on design and optimization of computer and telecommunications networks. He joined the University of Sydney in 1989 and became Professor of Imaging Science in 1997. He is currently Professor of Computer Engineering at City University of Hong Kong. His research interests include image processing, pattern recognition and bioinformatics. He is author or co-author of one book and over 200-refereed technical papers in these areas. Professor Yan is a fellow of the International Association for Pattern Recognition (IAPR), a fellow of the Institution of Engineers, Australia (IEAust), a senior member of the Institute of Electrical and Electronic Engineers (IEEE) and a member of the International Society for Computational Biology (ISCB).