Adaptive Sequential Prediction of Multidimensional Signals With Applications to Lossless Image Coding
ABSTRACT We investigate the problem of designing adaptive sequential linear predictors for the class of piecewise autoregressive multidimensional signals, and adopt an approach of minimum description length (MDL) to determine the order of the predictor and the support on which the predictor operates. The design objective is to strike a balance between the bias and variance of the prediction errors in the MDL criterion. The predictor design problem is particularly interesting and challenging for multidimensional signals (e.g., images and videos) because of the increased degree of freedom in choosing the predictor support. Our main result is a new technique of sequentializing a multidimensional signal into a sequence of nested contexts of increasing order to facilitate the MDL search for the order and the support shape of the predictor, and the sequentialization is made adaptive on a sample by sample basis. The proposed MDL-based adaptive predictor is applied to lossless image coding, and its performance is empirically established to be the best among all the results that have been published till present.
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ABSTRACT: A novel adaptive and exemplar-based approach is proposed for image restoration (denois- ing) and representation. The method is based on a pointwise selection of similar image patches of xed size in the variable neighborhood of each pixel. The main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood. We use small image patches (e.g. 7 7 or 9 9 patches) to compute these weights since they are able to capture local geometric patterns and texels seen in images. In this paper, we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error, at each spatial position. The proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered. The method is applied to articially corrupted real images and the performance is very close, and in some cases even surpasses, to that of the already published denoising methods. The proposed algorithm is demonstrated on real images corrupted by non-Gaussian noise and is used for applications in bio-imaging.International Journal of Computer Vision 01/2008; 79:45-69. · 3.62 Impact Factor
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ABSTRACT: This paper sheds light on the least-square (LS)-based adaptive prediction schemes for lossless compression of natural images. Our analysis shows that the superiority of the LS-based adaptation is due to its edge-directed property, which enables the predictor to adapt reasonably well from smooth regions to edge areas. Recognizing that LS-based adaptation improves the prediction mainly around the edge areas, we propose a novel approach to reduce its computational complexity with negligible performance sacrifice. The lossless image coder built upon the new prediction scheme has achieved noticeably better performance than the state-of-the-art coder CALIC with moderately increased computational complexityIEEE Transactions on Image Processing 07/2001; · 3.20 Impact Factor
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ABSTRACT: A new lossless intra coding method based on sample-by-sample differential pulse code modulation (DPCM) is presented as an enhancement of the H.264/MPEG-4 AVC standard. The H.264/AVC design includes a multidirectional spatial prediction method to reduce spatial redundancy by using neighboring samples as a prediction for the samples in a block of data to be encoded. In the new lossless intra coding method, the spatial prediction is performed based on samplewise DPCM instead of in the block-based manner used in the current H.264/AVC standard, while the block structure is retained for the residual difference entropy coding process. We show that the new method, based on samplewise DPCM, does not have a major complexity penalty, despite its apparent pipeline dependencies. Experiments show that the new lossless intra coding method reduces the bit rate by approximately 12% in comparison with the lossless intra coding method previously included in the H.264/AVC standard. As a result, the new method is currently being adopted into the H.264/AVC standard in a new enhancement project.IEEE Transactions on Image Processing 10/2006; 15(9):2610-5. · 3.20 Impact Factor