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Zuxing Xuan

Publications and source records attributed to Zuxing Xuan.

4 recordsLinked to original sources

PCA-SRGAN: Incremental Orthogonal Projection Discrimination for Face Super-resolution

Generative Adversarial Networks (GAN) have been employed for face super resolution but they bring distorted facial details easily and still have weakness on recovering realistic texture. To further improve the performance of GAN based models on super-resolving face images, we propose PCA-SRGAN which pays attention to the cumulative discrimination in the orthogonal projection space spanned by PCA projection matrix of face data. By feeding the principal component projections ranging from structure to details into the discriminator, the discrimination difficulty will be greatly alleviated and the generator can be enhanced to reconstruct clearer contour and finer texture, helpful to achieve the high perception and low distortion eventually. This incremental orthogonal projection discrimination has ensured a precise optimization procedure from coarse to fine and avoids the dependence on the perceptual regularization. We conduct experiments on CelebA and FFHQ face datasets. The qualitative visual effect and quantitative evaluation have demonstrated the overwhelming performance of our model over related works.

cs.CV

Fast Escaping Sets of meromorphic functions

In this paper, we give a definition of Eremenko's point of a meromorphic function with infinitely many poles and a condition for its existence in narrow annuli in terms of a covering theorem of annulus.

math.DS

A new geometric characterization of the Julia set

This article concerns a new geometric characterization of the Julia set. By using Ahlfors-Shimizu's characteristic, we establish some growth results which indicates the characterization of the Julia set. The main technique is to estimate the lower bound of $S(f^n,U)$, where $U$ is an open neighbourhood of some point in $\mathcal{J}(f)$.

math.DS

Common Borel radius of an algebroid function and its derivative

In this article, by comparing the characteristic functions, we prove that for any $ν$-valued algebroid function $w(z)$ defined in the unit disk with $\limsup_{r\to1-}T(r,w)/\log\frac{1}{1-r}=\infty$ and the hyper order $ρ_2(w)=0$, the distribution of the Borel radius of $w(z)$ and $w'(z)$ is the same. This is the extension of G. Valiron's conjecture for the meromorphic functions defined in $\widehat{\mathbb{C}}$.

math.CV