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Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

机译:用分段线性估计器解逆问题:从高斯混合模型到结构稀疏性

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摘要

A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.
机译:介绍了一种采用分段线性估计求解图像逆问题的通用框架。该方法基于高斯混合模型,该模型通过最大后验期望最大化算法进行估计。描述了使用结构化稀疏估计对提出的框架进行的双重数学解释,这表明与传统的稀疏逆问题技术相比,所得的分段线性估计使估计稳定。我们证明,在许多图像反问题中,包括窄核的插值,缩放和去模糊,相同的简单且计算效率高的算法产生的结果与现有技术相同。

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