全变分、自适应全变分和非凸平滑剪切绝对偏差惩罚用于块状图像去噪
Total Variation, Adaptive Total Variation and Nonconvex Smoothly Clipped Absolute Deviation Penalty for Denoising Blocky Images
AI总结：
针对全变分模型的偏差问题，提出一种受高维变量选择启发的非凸惩罚函数，通过MM算法高效求解，实验证明在块状图像去噪中性能优于传统方法。
摘要：
基于全变分的图像去噪模型已被广泛推广和扩展，在不同场景下提升了性能。我们提出一种新的惩罚函数，其灵感来自高维变量选择统计文献的最新进展。利用特定实例化的MM算法，优化问题可以高效求解，且计算过程与空间自适应全变分模型类似。我们的两像素图像模型从理论上证明，新惩罚函数解决了全变分模型固有的偏差问题。通过多个实验展示了新惩罚的优越性能。我们的研究仅限于具有小全变分的“块状”图像。
英文摘要：
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical literature on high-dimensional variable selection. Using a particular instantiation of the majorization-minimization algorithm, the optimization problem can be efficiently solved and the computational procedure realized is similar to the spatially adaptive total variation model. Our two-pixel image model shows theoretically that the new penalty function solves the bias problem inherent in the total variation model. The superior performance of the new penalty is demonstrated through several experiments. Our investigation is limited to "blocky" images which have small total variation.
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