This paper addresses single image super-resolution (SR) based on convolutional neural networks (CNNs). It is known that recovery of high-frequency components in output SR images of CNNs learned by the least square errors or least absolute errors is insufficient. To generate realistic high-frequency components, SR methods using generative adversarial networks (GANs), composed of one generator and one discriminator, are developed. However, when the generator tries to induce the discriminator's misjudgment, not only realistic high-frequency components but also some artifacts are generated, and objective indices such as PSNR decrease. To reduce the artifacts in the GAN-based SR methods, we consider the set of all SR images whose square errors between downscaling results and the input image are within a certain range, and propose to apply the metric projection onto this consistent set in the output layers of the generators. The proposed technique guarantees the consistency between output SR images and input images, and the generators with the proposed projection can generate high-frequency components with few artifacts while keeping low-frequency ones as appropriate for the known noise level. Numerical experiments show that the proposed technique reduces artifacts included in the original SR images of a GAN-based SR method while generating realistic high-frequency components with better PSNR values in both noise-free and noisy situations. Since the proposed technique can be integrated into various generators if the downscaling process is known, we can give the consistency to existing methods with the input images without degrading other SR performance.

The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

This paper proposes a high-quality computed tomography (CT) image reconstruction method from low-dose X-ray projection data. A state-of-the-art method, proposed by Xu et al., exploits dictionary learning for image patches. This method generates an overcomplete dictionary from patches of standard-dose CT images and reconstructs low-dose CT images by minimizing the sum of a data fidelity and a regularization term based on sparse representations with the dictionary. However, this method does not take characteristics of each patch, such as textures or edges, into account. In this paper, we propose to classify all patches into several classes and utilize an individual dictionary with an individual regularization parameter for each class. Furthermore, for fast computation, we introduce the orthogonality to column vectors of each dictionary. Since similar patches are collected in the same cluster, accuracy degradation by the orthogonality hardly occurs. Our simulations show that the proposed method outperforms the state-of-the-art in terms of both accuracy and speed.