Tensor based methods have been used in a wide range of signal processing applications. A particular area of interest is tensor decomposition, which can be used to reduce the dimensionality of the massive multidimensional data. Hence, tensor decomposition can be considered as a high dimension extension of popular Singular Value Decomposition (SVD) methods used for matrix analysis. The lower dimension representation of tensors resulting from tensor decomposition can be used for classification, pattern recognition, and reconstruction. Our objective in the first part of this thesis, is to develop a tensor coding framework based on a tensor decomposition method for visual data efficient representation and compression. As part of the proposed tensor coding framework, we developed a tensor decomposition algorithm that decomposed the input tensor into a set of rank-one tensors. The proposed decomposition is designed to be efficient specifically for visual data. The proposed tensor decomposition algorithm is applied in a block-wise approach. Two partitioning methods are proposed for tensor coding framework which are uniform and adaptive tree partitioning. The former subdivide a region into a set of equal size blocks while the later subdivide a region into a set of variable size blocks. The decision whether to subdivide the region or not is made based on the existing amount of the information and the overall available bitrate. A tree data structure stores the partitioning structure information which is required for the tensor reconstruction process.Furthermore, an encoder/decoder framework is proposed for compressing and storing the decomposed data. The proposed framework provides a number of desirable properties especially at the decoder side which can be critical for some applications. Low complexity reconstruction, random access, and scalability are the main properties that we have targeted. We demonstrate the viability of the proposed tensor coding framework by employing it for the representation and coding of three types of data sets: hyperspectral/multispectral images, bio-metric face image ensembles, and low motion videos. These data sets can be arranged as either three or four dimensional tensors. For each application, we show that the compression efficiency along with the inherited properties of the proposed tensor coding framework, provide a competitive approach to the current standard methods. In the second part of the thesis, we propose an example-based super-resolution algorithm for a new framework of scalable video streaming. The proposed method is applicable to scalable videos where the enhancement layer of some frames might be dropped due to changing network conditions. This leads to a streaming scenario that we call Inconsistent Scalable Video (ISV) streaming. At the decoder, the frames with the enhancement layer are used as a dictionary for super-resolving other video frames whose enhancement layers were dropped. The proposed super-resolution framework is integrated with Google VP9 video codec. Then it is applied to various High Definition (HD) videos to estimate the dropped enhancement layer. Our simulation results show an improvement visually and in terms of PSNR over traditional interpolation up-sampling filters.
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