图像复原中什么是数据保真项？什么是先验项？

在机器学习里，经常会看到两个词，data fidelity term, regularization(prior) term.

例如，在image restoration中，我们需要最小化如下的object function(MAP, 最大后验概率)，则：

$\widehat{x}=arg \, \underset{x}{min}\frac{1}{2}\, \left \| y-Hx \right \|\, +\, \lambda \Phi (x)$

data fidelity term: $\frac{1}{2}\left \| y-Hx \right \|$

regularization(prior) term: $\lambda \Phi (x)$

那么两项的作用是什么呢？

The fidelity term guarantees the solution accords with the degradation process,

翻译：数据保真项保证结果符合降质过程

while the regularization term enforces desired property of the output.

翻译：正则（先验）项对输出进行增强

Since IR is an ill-posed inverse problem, the prior which is also called regularization needs to be adopted to constraint the solution space

翻译：因为image restoration是病态解问题，所以用正则（先验）项限制解空间