Kompresja Cyfrowych Sekwencji Wizyjnych z Wykorzystaniem Poszukiwania Dopasowującego dla Reprezentacji Separowalnych

The problem of optimal approximation of function with a linear expansion using overcomplete dictionary of non-orthogonal waveforms is NP-hard. Matching pursuit, introduced by Mallat and Zhang, is a greedy sub-optimal algorithm for finding an approximate solution to the above problem. This technique has been adopted by Neff and Zakhor as an alternative to the conventional DCT-based method for coding a prediction error frame. Despite the greedy strategy, the most significant problem of the matching pursuit is its intensive computation in the encoding step. Therefore, many assumptions and limitations-as separability of functions from dictionary-are applied in real-world applications. Nevertheless, despite limitations and assumptions, the computational load of matching pursuit is still huge. In addition, another fundamental problem of matching pursuit, i.e. the lack of feedback between an input signal and a dictionary, still exists. Therefore, in order to break through the drawbacks of the matching pursuit, in the thesis of the dissertation, new strategy for searching atoms is proposed. The key element of this technique is separable decomposition that allows for computing a separable function that minimises the Euclidean norm of approximation error. The results showed that the proposed algorithm is over seven times faster than the classic matching pursuit algorithm. Additionally, the novel algorithm allows for designing a dictionary. Dictionaries obtained using a proposed learning scheme, outperforms the dictionary proposed by Neff and Zakhor in term of PSNR. The experiments confirmed that the separable decomposition efficiently exploits separability of an input signal and gives a way to improve the representational performance of a dictionary. Moreover, the learning scheme described in the dissertation, gives great support for experiments. An important observation is that the highly redundant dictionary does not improve the quality of approximation. The experimentally obtained results indicate the bound of the number of separable functions in the dictionary that makes compression process unattractive. This fact means that further improvement in signal approximation lies in adequate prediction or adaptation to a current context i.e. to the frame or to the region of frame. The proposal for image-adapted dictionary is also presented in the dissertation. Results obtained by using dynamic dictionary adapted to the context of frame prove high compression efficiency of such system.