Distributed image and video coding based on compressed sensing : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Engineering at Massey University, New Zealand

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Massey University
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Conventional methods for encoding of images and videos is a complex process with high computational demands. They are designed for application scenarios where the signals concerned are encoded once and played back many times. However, new applications such as wireless video sensor networks demand low cost and low power cameras with limited computing resources. The focus of this thesis is on such image and video coding systems where the computational burden is shifted from the encoder to the decoder. Three separate coding schemes have been developed { two for videos and one for images. Together they form a framework for distributed coding which is based on the theory of compressed sensing and distributed coding. Compressed sensing is a relatively new theory for the acquisition of sparse signals that allows the sampling rate to be much lower than the Nyquist limit. Distributed coding is based on the theorem by Slepian and Wolf, and Wyner and Ziv. It allows different correlated parts of a signal to be encoded independently without loss of coding efficiency. The decoding of these separately encoded parts are then decoded jointly in order to exploit the correlation between them. The main characteristics of the coding scheme proposed in this thesis are: (1) they do not require the use of traditional codecs; (2) only compressed sensing measurements are used for encoding and decoding; (3) no motion estimation and compensation are involved for videos. The first proposed coding scheme is for the encoding of whole video frames. The compressed sensing measurement of individual frames are separately encoded. These frames are divided into key and non-key frames with the key frames encoded at a higher rate than non-key ones. While the key frames are decoded independently, the non-key ones are decoded with the help of side information generated from the measurements of the key frames. The most important part of the decoder is a simple, yet effective, side information generation method which requires only minimal computation. The side information generated is simply added to the measurements of the non-key frames for use with any compressed sensing reconstruction algorithm. The other two coding schemes are block-based coding methods. Each image or frame is divided into non-overlapping image blocks in a similar way it is done in some existing coding standards. The coding of the blocks are performed in a distributed manner by classifying them into key blocks and nonkey blocks. An adaptive encoding strategy based on block similarity is also developed. Experimental analyses using publicly available test images and videos show that the performances of the simpler codecs proposed are better than other existing compressed sensing based codecs. The video codecs also out-perform conventional distributed video codec in terms of simplicity, compression ratio and decoding complexity. The basis of these coding methods is on the correlation of frames or blocks. This correlation is established through experimental analyses. These analyses also showed that the minimum square error between any pair of them can be effectively used as a measure of correlation. In conjunction with the development of the codecs, a quantization scheme that is tailored to the statistics of CS measurements has also been proposed. This scheme yields better results than a uniform quantizer and those used for JPEG. The quantizer is also robust against different statistics of individual images. Separate experimental evaluations also show that structurally random matrices are the best sensing matrices for acquiring images and the sparse reconstruction by separable approximation (SpaRSA) algorithm produces the best reconstructed image quality.
Signal processing, Coding theory, Image processing, Video compression