能量泛函正则化模型在图像恢复中的应用分析

目的 能量泛函正则化模型是图像恢复研究的热点。为使更多工程领域的研究者对正则化技术进行探索和应用，推动不适定问题的研究，对能量泛函正则化模型的进展进行了分析。方法 首先建立图像整体坐标与局部坐标的关系，分析图像恢复正则化模型的基本原理，给出并证明正则化模型各向同性与各向异性扩散定理。然后结合函数空间、图像分解和紧框架，评述能量泛函正则化模型国内外发展现状，并对正则化模型解的适定性进行分析。结果 推导出图像恢复正则化模型扩散基本原理，给出正则化模型通用表达式，讨论正则化模型存在的问题及未来的发展方向。结论 正则化技术在解决图像恢复、修复等反问题起着重要作用。目前，国内外学者对该问题的研究取得了一些成果，但许多理论问题有待进一步研究。

Application analysis of regularization model of energy functional to image restoration

Objective Energy functional regularization model is an active research field in image restoration. To draw more attention from researchers of engineering community, and to push forward the research of the ill-posed problem, the paper provides a comprehensive analysis of recent development on regularization model of image restoration.Method Firstly, the relationship between total coordinate and local coordinate of image is established, and the principle of regularization term of image restoration is analyzed, and the isotropic and anisotropic diffusion theorems of regularization model are given. Secondly, based on functional space, image decomposition and tight frame, the disadvantages and advantages of the regularization models are analyzed, and the state of the art Methods are reviewed. Furthermore, the well-posed properties of solution of regularization model are analyzed.Result The basic diffusion principles of image restoration regularization model are deduced, the general formulas of regularization model are given, the potential problems and future development trends are discussed.Conclusion Regularization technology plays a key role in opposite problem research, such as image restoration and inpainting, currently, though some excellent Results have been reported, many theory challenges still need to be investigated.