Single image super-resolution (SISR) is a notoriously challenging ill-posed problem that aims to obtain a highresolution (HR) output from one of its low-resolution (LR) versions. Recently, powerful deep learning algorithms have been applied to SISR and have achieved state-of-the-art performance. In this survey, we review representative deep learning-based SISR methods and group them into two categories according to their contributions to two essential aspects of SISR: the exploration of efficient neural network architectures for SISR and the development of effective optimization objectives for deep SISR learning. For each category, a baseline is first established, and several critical limitations of the baseline are summarized. Then, representative works on overcoming these limitations are presented based on their original content, as well as our critical exposition and analyses, and relevant comparisons are conducted from a variety of perspectives. Finally, we conclude this review with some current challenges and future trends in SISR that leverage deep learning algorithms.

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This paper presents a fully automatic three-dimensional classification of brain tissues for Magnetic Resonance (MR) images. An MR image volume may be composed of a mixture of several tissue types due to partial volume effects. Therefore, we consider that in a brain dataset there are not only the three main types of brain tissue: gray matter, white matter, and cerebro spinal fluid, called pure classes, but also mixtures, called mixclasses. A statistical model of the mixtures is proposed and studied by means of simulations. It is shown that it can be approximated by a Gaussian function under some conditions. The D'Agostino-Pearson normality test is used to assess the risk alpha of the approximation. In order to classify a brain into three types of brain tissue and deal with the problem of partial volume effects, the proposed algorithm uses two steps: 1) segmentation of the brain into pure and mixclasses using the mixture model; 2) reclassification of the mixclasses into the pure classes using knowledge about the obtained pure classes. Both steps use Markov random field (MRF) models. The multifractal dimension, describing the topology of the brain, is added to the MRFs to improve discrimination of the mixclasses. The algorithm is evaluated using both simulated images and real MR images with different T1-weighted acquisition sequences.

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GAN inversion aims to invert a given image back into the latent space of a pretrained GAN model, for the image to be faithfully reconstructed from the inverted code by the generator. As an emerging technique to bridge the real and fake image domains, GAN inversion plays an essential role in enabling the pretrained GAN models such as StyleGAN and BigGAN to be used for real image editing applications. Meanwhile, GAN inversion also provides insights on the interpretation of GAN's latent space and how the realistic images can be generated. In this paper, we provide an overview of GAN inversion with a focus on its recent algorithms and applications. We cover important techniques of GAN inversion and their applications to image restoration and image manipulation. We further elaborate on some trends and challenges for future directions. A curated list of GAN inversion methods, datasets, and other related information can be found at github.com/weihaox/awesome-gan-inversion.

For two-class discrimination, Ref.~\cite{Xie:2007} claimed that, when covariance matrices of the two classes were unequal, a (class) unbalanced dataset had a negative effect on the performance of linear discriminant analysis (LDA). Through re-balancing $10$ real-world datasets, Ref.~\cite{Xie:2007} provided empirical evidence to support the claim using AUC (Area Under the receiver operating characteristic Curve) as the performance metric. We suggest that such a claim is vague if not misleading, there is no solid theoretical analysis presented in~\cite{Xie:2007}, and AUC can lead to a quite different conclusion from that led to by misclassification error rate (ER) on the discrimination performance of LDA for unbalanced datasets. Our empirical and simulation studies suggest that, for LDA, the increase of the median of AUC (and thus the improvement of performance of LDA) from re-balancing is relatively small, while, in contrast, the increase of the median of ER (and thus the decline in performance of LDA) from re-balancing is relatively large. Therefore, from our study, there is no reliable empirical evidence to support the claim that a (class) unbalanced data set has a negative effect on the performance of LDA. In addition, re-balancing affects the performance of LDA for datasets with either equal or unequal covariance matrices, indicating that having unequal covariance matrices is not a key reason for the difference in performance between original and re-balanced data.