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A new greedy sparse recovery algorithm for fast solving sparse representation
The Visual Computer ( IF 3.5 ) Pub Date : 2021-04-17 , DOI: 10.1007/s00371-021-02121-6
Zied Bannour Lahaw , Hassene Seddik

Kernel sparse representation-based classification (KSRC) in compressive sensing represents one of the most interesting research areas in pattern recognition and image processing. Nevertheless, KSRC is subjected to some shortcomings. KSRC is greedy in time to achieve an approximate solution of sparse representation based on \(\ell_{1}\)-norm minimization. A diversity of greedy recovery algorithms have been tested in order to decrease computational complexity compared to the optimal \(\ell_{1}\)-norm minimization while keeping a proved reconstruction accuracy. In this research, we suggest a new greedy recovery algorithm, called the fast reduced sampling matching pursuit (FRSMP). Unlike previous greedy recovery algorithms which applied too many or very few values per iteration, FRSMP selects a sufficient number of elements. Moreover, FRSMP performs the least square minimization iteratively through the Sherman–Morrison–Woodbury formula, to avoid large matrix inversion which results in a significant speedup. Experimental results with both noisy and noiseless data have shown that the proposed FRSMP method achieves a higher reconstruction accuracy at low reconstruction time compared to other greedy pursuit algorithms. Also, experiments on frequent face databases have proven that the KSRC-based FRSMP method shows reliable and higher recognition rate and computation time compared with other advanced sparse representation methods for face recognition.



中文翻译:

快速求解稀疏表示的新贪婪稀疏恢复算法

压缩感知中基于核稀疏表示的分类(KSRC)代表了模式识别和图像处理中最有趣的研究领域之一。但是,KSRC存在一些缺点。KSRC在时间上贪婪以基于\(\ ell_ {1} \)- norm最小化来实现稀疏表示的近似解决方案。与最佳\(\ ell_ {1} \)相比,已经测试了多种贪婪恢复算法,以降低计算复杂度-范数最小化,同时保持已证明的重构精度。在这项研究中,我们建议一种新的贪婪恢复算法,称为快速减少采样匹配追踪(FRSMP)。与以前的贪婪恢复算法(每次迭代使用太多或很少的值)不同,FRSMP选择足够数量的元素。此外,FRSMP通过Sherman-Morrison-Woodbury公式迭代执行最小二乘最小化,以避免大型矩阵求逆,从而显着提高了速度。带有噪声和无噪声数据的实验结果表明,与其他贪婪追踪算法相比,所提出的FRSMP方法在较短的重建时间上实现了更高的重建精度。还,

更新日期:2021-04-18
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