| Popis: |
This paper introduces two variants of the backward replacement approach, T-BRe and H-BRe, aimed at enhancing the compression capabilities of forward greedy pursuit algorithms. The effectiveness of these methods is evaluated using three greedy pursuit algorithms (OMP, OOMP, and FBP) through simulations conducted on image and speech datasets with a mathematically generated dictionary. Additionally, a mathematical analysis of the H-BRe algorithm is provided to validate its effectiveness and address inherent limitations. Both analysis and simulations confirm that the H-BRe algorithm significantly improves the compression capabilities of forward greedy pursuit algorithms. The degree of enhancement varies depending on factors such as the forward modeling technique, stopping criterion, and the stochastic nature of the backward replacements. The high-performance (H) variants demonstrate superior performance across various modeling approaches, as evidenced by metrics such as PESQ and SSIM values, while the B and T variants also exhibit efficiency in specific scenarios. Despite these promising results, our methods encounter limitations such as time complexity, local error minimization, dependence on atom types, and the assumption of linear distribution. Future research directions include optimizing time complexity, balancing compression-quality trade-offs, globally minimizing replacement errors, exploring diverse atom types, and refining mathematical assumptions to further elucidate H-BRe’s performance characteristics. |
