论文标题
稳定图像重建的总变异最小化
Enhanced total variation minimization for stable image reconstruction
论文作者
论文摘要
总变化（TV）正则化显着增强了图像处理任务的各种变异模型。我们建议将图像增强的早期文献中的向后扩散过程与电视正则化结合，并表明所得增强的电视最小化模型对于减少对比度的丧失特别有效。本文的主要目的是通过两种采样策略，通过两种采样策略，非适应性采样来为增强的电视模型建立稳定的重建保证，用于一般线性测量和用于傅立叶测量的可变密度采样。特别是，在某些较弱的等轴测属性条件下，增强的电视最小化模型比在噪声级别显着且测量量的情况下的各种基于电视的模型显示出更严格的重建误差界限。增强电视模型的优势也通过重建某些合成，自然和医学图像的初步实验在数值上验证。
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV regularization, and show that the resulting enhanced TV minimization model is particularly effective for reducing the loss of contrast. The main purpose of this paper is to establish stable reconstruction guarantees for the enhanced TV model from noisy subsampled measurements with two sampling strategies, non-adaptive sampling for general linear measurements and variable-density sampling for Fourier measurements. In particular, under some weaker restricted isometry property conditions, the enhanced TV minimization model is shown to have tighter reconstruction error bounds than various TV-based models for the scenario where the level of noise is significant and the amount of measurements is limited. Advantages of the enhanced TV model are also numerically validated by preliminary experiments on the reconstruction of some synthetic, natural, and medical images.
