基于小波的多层框架用于ℓ₁正则化图像去模糊
Wavelet-based multilevel framework for $\ell_1$-regularized image deblurring
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中文总结 AI 辅助
针对大规模ℓ₁正则化图像去模糊的计算挑战，提出嵌入三种迭代求解器的小波多层框架，对比两种信息传递策略，实验验证其计算效率提升效果。
中文摘要 AI 辅助
高效求解大规模ℓ₁正则化图像去模糊问题同时保留清晰边缘仍是重大计算挑战。我们提出一种基于小波的多层框架，在多层V循环中嵌入三种迭代求解器：迭代重加权最小二乘法（IRLS）、分裂布雷格曼法（SB）和 majorization-minimization法（MM）。离散小波变换定义层间传递算子，正则化参数通过广义交叉验证自动选择。引入并比较两种信息传递策略：一种仅将粗层解传递到细层，另一种传递求解器特有的辅助量。数值实验表明，IRLS可实现显著计算节省，加速比超一个数量级，而MM和SB的计算差异更温和。实验总体显示，采用Haar小波时传递辅助迭代量效果最佳，采用Daubechies小波时仅传递解效果最佳。
英文摘要
Solving large-scale $\ell_1$-regularized image deblurring problems efficiently while preserving sharp edges remains a significant computational challenge. We propose a wavelet-based multilevel framework that embeds three iterative solvers, Iteratively Reweighted Least Squares (IRLS), Split Bregman (SB), and Majorization-Minimization (MM), within a multilevel V-cycle. Discrete wavelet transforms define the interlevel transfer operators, and regularization parameters are selected automatically by Generalized Cross Validation. Two information transfer strategies are introduced and compared: one transfers only the coarse solution to the fine level, while the other transfers solver-specific auxiliary quantities. Numerical experiments demonstrate substantial computational savings for IRLS, with speedups exceeding an order of magnitude, while MM and SB exhibit more modest computational differences. The experiments generally show that transferring auxiliary iterates performs best with Haar wavelets, whereas transferring only the solution performs best with Daubechies wavelets.
