X-GAN
Image reconstruction including image restoration and denoising is a challenging problem in the field of image computing. We present a new method, called X-GANs, for reconstruction of arbitrary corrupted resource based on a variant of conditional generative adversarial networks (conditional GANs). In our method, a novel generator and multi-scale discriminators are proposed, as well as the combined adversarial losses, which integrate a VGG perceptual loss, an adversarial perceptual loss, and an elaborate corresponding point loss together based on the analysis of image feature. Our conditional GANs have enabled a variety of applications in image reconstruction, including image denoising, image restoration from quite a sparse sampling, image inpainting, image recovery from the severely polluted block or even color-noise dominated images, which are extreme cases and haven’t been addressed in the status quo. We have significantly improved the accuracy and quality of image reconstruction. Extensive perceptual experiments on datasets ranging from human faces to natural scenes demonstrate that images reconstructed by the presented approach are considerably more realistic than alternative work. Our method can also be extended to handle high-ratio image compression. …

Transfinite Mean
We define a generalization of the arithmetic mean to bounded well-ordered sequences of real numbers. We show that every probability space admits a well-ordered sequences of points such that the measure of each measurable subset is equal to the frequency with which the sequence is in this subset. We include an argument suggested by Woodin that the club filter on $\omega_1$ does not admit such a sequence of order type $\omega_1$. …

Probit Model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit.[1] The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for an ordinal[2] or a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. The probit model, which employs a probit link function, is most often estimated using the standard maximum likelihood procedure, such an estimation being called a probit regression. …

Soft Computing (SC)
Soft computing is a term applied to a field within computer science which is characterized by the use of inexact solutions to computationally hard tasks such as the solution of NP-complete problems, for which there is no known algorithm that can compute an exact solution in polynomial time. Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for soft computing is the human mind. …