الفهرس 
Discrete Backward Stage (DBS)Only 14 pages are availabe for public view
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Abstract
In this thesis, we introduce three contributions in the field of sparse-based speech compression. The main contribution of this thesis is introducing a new backward technique so-called the Backward Replacement (BRe) that takes into consideration the impact of backward processing on the signal compression. The new technique doesn’t exploit the correlations to eliminate the weights, but it exploits the converged weights to replace the sparse vector with a sparse symmetric matrix which could be encoded efficiently. As for the second contribution, we introduce a lossy-based rate saving enhancement on the BRe using an optimized approach that exploits the correlation among the atoms to reduce the replacement errors. Finally, we introduce a lossless-based rate saving enhancements which is based on hiding rows and columns in the obtained sparse matrix during the index encoding process.
By comparing our approach with the backward elimination algorithms in the field of speech compression we concluded that, the BRe enhanced the compression capabilities of the forward modeling by 47% and outperforms the other backward elimination techniques whose enhancements reaches at most 15%. Also, from the obtained results we proved that, the proposed algorithm have the ability of encoding the speech signals at different bit rates with a reasonable quality. Not only, the proposed strategy proved its effectiveness on the compression but also it has a low complexity in comparison to the elimination-based backward algorithms.
As for the second and third contributions in this study, they are considered trials to enhance the rate savings of the OMP-BRe coder. The second contribution is a lossy-based RS enhancement approach and is termed the Optimized BRe (OBRe). The corresponding coder of this approach is termed OMP-OBRe and the results proved that, it has demonstrated successfully the superiority over OMP-BRe coder in enhancing the rate savings under certain conditions by approximately 3%, but in return, there is more computation time needed to fulfill the backward process. As for the third contribution, it is a lossless-based RS enhancement approach, and the results proved that the enhancements obtained by this approach are weak and don’t exceed 1%.