Adaptive Geometric Duality(AGD) Prior

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由于对SR的实现方法不了解，关于SR部分基本是定性的描述。
AGD即：在实现SR插值过程中，能根据LR自动计算某些权值，使的到的HR和LR满足“几何对偶”的先验规律，例如稳健软判决插值（Robust Soft-Decision Interpolation）就是被认为是一种杰出的AGD方法。

下面简单解释了什么是GD，以及如何得到自适应权值

geometry duality

[2012] (TIP)Robust Soft-Decision Interpolation Using Weighted Least Squares

SAI relies on “geometric duality” (i.e., the consistency of geometric structure across resolutions) to estimate HR parameters using LR samples

For parameter estimation, the weighting criteria are specifically designed according to the definition of “geometric duality”

以减少几何对偶的不匹配为约束条件，在实现SR的过程中就可以调整一些参数和权值使LR与HR更好的满足“几何对偶”先验特性。

adaptive GD weighted

[2016] (TIP)Single Image Super-Resolution Using Local Geometric Duality and Non-Local Similarity
By assembling the two complementary strategies, an adaptive geometric duality (AGD) prior is presented, which primarily relies on the proposed luminance-difference-based local non-smoothness detection method and the directional standard-deviation-based weights selection method

计算出的Xi在[0,1]之间，图像块越平滑就越接近于0，反之则接近于1

最后将计算出的Xi和Ui用在插值方法中，使得SR后得到的HR图像与参考图像更相近

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