Digital images and videos undoubtedly contribute a big trunk in digital multimedia data people are enjoying today. Since the digital representation of raw image and video signals requires a huge capacity, tremendous coding algorithms have been developed to efficiently represent signals for storage and transmission purposes. In this thesis, three advanced techniques for image and video coding are investigated: directional discrete cosine transform (DDCT), spectral recovery for compressed image restoration, and compressive sensing....[ Read more ]

Digital images and videos undoubtedly contribute a big trunk in digital multimedia data people are enjoying today. Since the digital representation of raw image and video signals requires a huge capacity, tremendous coding algorithms have been developed to efficiently represent signals for storage and transmission purposes. In this thesis, three advanced techniques for image and video coding are investigated: directional discrete cosine transform (DDCT), spectral recovery for compressed image restoration, and compressive sensing.

Among various coding algorithms, the block-based transform coding is widely employed in image and video compression owing to its simplicity, excellent energy compaction in the transform domain, and super compromise between bit-rate and quantization errors. In our DDCT, the directionality (other than vertical and horizontal) of each image block is taken into consideration. Consequently, a new block-based transform framework is proposed, in which the first transform may choose to follow a direction other than the vertical or horizontal one. The coefficients produced by each directional transform are arranged into a column vector so that the second transform is applied to all coefficients that are aligned horizontally. By selecting the best transform mode, each image block is encoded with less bits and/or higher quality. Furthermore, the advantages of the developed DDCT are substantiated by some theoretical analysis on the coding gain and energy packing efficiency. In addition, a novel directional decoding algorithm is developed to enhance the visual quality of the compressed images.

Information loss is unavoidable due to the limitation on the transmission bandwidth or storage capacity. Hence, the correlation within signals cannot be re-built accurately to some extent, especially the annoying artifacts introduced in the block-based transform coding schemes. By exploring the cross-domain correlation within the compressed images, we introduce a novel spectral prediction algorithm to restore lossy spectral information caused by compression. The relationship among cross-frequency coefficients is adopted to predict spectral coefficients, and the spectral recovery through the total variation (TV) based regularization is confined by the reliable coefficient evaluation range. Accordingly, remarkable improvement on visual quality can be observed in the experimental results.

The recent theory of compressive sensing reveals that a sparse signal can be recovered by randomly taking a small number of measurements. Since the compressive sensing is distinct from the traditional coding algorithms, it is crucial to answer the question whether the compressive sensing can enhance the coding efficiency by random sampling the sources. For the sake of simplicity, we analyze the coding performance of the compressive sensing for binary sparse sources. Two models are applied to describe the random sampling and recovery process: the bipartite graph and the tree structure. Based on the bipartite graph model, we derive the closed-form formulas for the node and edge evolutions. With the closed-form formulas, we further analyze the conditions for successful decoding and formulate the distortion calculation. In the analysis on the tree structure model, the recovery distortion is evaluated by the un-recovery probability, and the same conditions of a successful recovery are deduced.