Digital image deblurring with SOR
Digital image deblurring with SOR
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DOI：
10.1088/0266-5611/24/2/025024
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发表时间：
2008-03
期刊：
影响因子：
2.1
通讯作者：
V N Strakhov;S V Vorontsov
中科院分区：
文献类型：
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作者：
V N Strakhov;S V Vorontsov
我们解决的连续超松弛技术（SOR）在天文图像恢复的数值性能。局部分析的收敛率揭示了共振特性，与收敛增强的空间频率，这是由SOR弛豫参数τ。该分析可以作为松弛参数的实际选择的指导，该松弛参数控制SOR算法的正则化性质。一个特定的预测是，在典型的实现中，快速图像去模糊需要深度欠松弛（τ ε 1）。这一理论结果使我们能够更好地理解生产性能的欠松弛，这已经发现在早期的工作。SOR在人工反演与共轭梯度和相关方法（GMRES）的比较表明，类似或更好的质量的解决方案，可以在一个可比的或更少的迭代次数。用非负约束（+SOR）约束解，既提高了解的质量，又提高了收敛速度。然而，+SOR的收敛特性的理论分析，仍然是一个挑战，不能解决的简单的分析实现本文。
We address the numerical performance of the successive overrelaxation technique (SOR) in the restoration of astronomical images. Local analysis of the convergence rates reveals resonant properties, with convergence enhancement at a spatial frequency which is determined by the SOR relaxation parameter τ. The analysis can serve as a guide for the practical choice of the relaxation parameter(s), which governs the regularization properties of the SOR algorithm. One particular prediction is that in typical implementations, fast image deblurring requires deep underrelaxation (τ ≪ 1). This theoretical result allows us to better understand the productive properties of underrelaxation, which have been discovered in earlier work. Comparison of SOR in artificial inversions with conjugate gradients and related methods (GMRES) indicates that a solution of similar or better quality may be obtained in a comparable or smaller number of iterations. Restricting the solution with non-negativity constraint (+SOR) enhances both the quality of the solutions and the convergence rate. Theoretical analysis of the convergence properties of +SOR, however, remains a challenge which cannot be addressed by the simple analysis implemented in this paper.