Studies On Adaptive Transforms For High Performance Image Coding

With the continuous increase of the image resolution and emergences of new image representations, data volumns of digital images keep increasing. Thus, there is a continuous requirement to improve the coding performance of image coding. Thus, as a key component in most image coding systems, transforms play an important role for the further development of image coding technologies. However, in nowadays image coding systems, in some aspects, the transforms lack of adaptivity to better exploit the correlation within image signals. In this dissertation, we focus on adaptive transform strcuctures and adaptive directional transforms to design new transforms for more efficient image coding methods.In block-based coding systems, by analyzing the inter-block prediction and conventional transform, we generalize the inter-block prediction and the intra-block transform to form a unified representation, which is called intra predictive transforms. Thus, an intra predictive transform not only can exploit correlations within the current block, it can also exploit the inter-block correlation. To evaluate the coding capacity of intra predictive tranforms, we analyze the coding performance for static signals by the coding gain of an intra predictive transform. In theory, we derive the upper bound of the coding gain of intra predictive transforms. It turns out that the upper bound of the coding gain depends only on the statistics of the input signals and is much larger than that of conventional transforms. Then we construct an optimal intra predictive transform which can achieve the upper bound of the coding gain. Thus, the upper bound is tight. The representation of intra predictive transforms also gives us a new angle to design new transforms for coding. As an example, we design an intra predictive transform which uses frequency domain prediction but has much shorter prediction distance than conventional frequency domain predictions. Experiemtal results verify the effectiveness of the new transform.By using the intra predictive transform theory, we are able to analyze the coding performance of different coding structures. Specially, we are interested in the block-based, line-based and pixel-based coding structures. We use the theory developed for intra predictive transforms to analyze coding gains of different coding structures. The theoretical results show that at high bit-rates, all these three coding structures can achieve the same coding gain, which is the upper bound of the coding gain of the block-based coding structure. We further generalize this conclusion to any possible coding structure. Thus, the result justifies that we should investigate other coding structures besides the block-based one, which dominates the image/video coding schemes nowadays. Then, we further analyze the pros and cons of different coding structures at middle or low bit-rates and in practical coding. The conclusion is that block-based structure may be more suitable for low bit-rate coding, while the other two can show more adaptivity and flexibility in coding. Based on the analysis, we design a high performance line-based image coding scheme and a pixel-based scheme. Experimental results show that they can provide comparable coding performance even compared to the state-of-the-art intra frame coding scheme. At high bit-rates, they can even outperform the state-of-the-art. Realizing that different structures have their advantages and disadvantages, we further propose a hybrid structure image coding scheme, which can fully utilize these three coding structures. Experiemental results demonstrate a remarkable improve in coding performance compared to the state-of-the-art.Besides structure adaptivity, the other property we investigate is directional adaptivity. Images are full of different directional information. However, conventional transforms cannot efficiently represent directional information since they lack directional base functions. By using lifting factorization, we factorize lapped transforms into elementary operators. By applying each operator directionally, we construct corresponding directional lapped transforms. We not only design 1-D and 2-D directional lapped transform, we also design block adaptive directional transform for different content in images. We model the direction selection as a rate-distortion optimization. By appropriate simplifications, we show that the direction selection in image coding using directional lapped tranforms can be solved by a dynamic programming algorithm. By integrating the block-adaptive lapped transform and corresponding direction selection algorithm into HD Photo (or JPEG-XR), the coding performance can be significantly improved, especially for images which contain much directional information.In directional wavelet transforms, the adaptivety can also include subsampling adaptivity since subsampling may influence the capability of the transform to exploit the directionality, which is not shown in conventional transforms. Thus, the problem that subsampling can influence much on the performance of directional wavelet transforms is raised in this dissertation. Then we perform indeep investigation and analysis on this problem. The result shows that the relation between the most suitable subsampling and the input signals is complicated. It is influenced by both the direction and also the correlation strength. Based on the analysis, we further design a subsampling-adaptive directional wavelet transform which can better exploit various directional correlations. To handle the boundary issues when subsampling changes, a phase-completion method is proposed. Experiemntal results show that the proposed transform can significantly improve the coding performance of directional wavelet transforms in JPEG 2000 coding system.