Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR). Existing SR methods either learn the prior from the low/high-resolution patch pairs or estimate the prior models from the input low-resolution (LR) image. Specifically, high-frequency details are learned in the former methods. Though effective, they are heuristic and have limitations in dealing with blurred LR images; while the latter suffers from the limitations of frequency aliasing. In this paper, we propose to combine those two lines of ideas for image super-resolution. More specifically, the parametric sparse prior of the desirable high-resolution (HR) image patches are learned from both the input low-resolution (LR) image and a training image dataset. With the learned sparse priors, the sparse codes and thus the HR image patches can be accurately recovered by solving a sparse coding problem. Experimental results show that the proposed SR method outperforms existing state-of-the-art methods in terms of both subjective and objective image qualities.

In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximizes information about a'relevance' variable,

Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR).

Neural Information Processing Systems http://nips.cc/

ABSTRACT Scientific datasets often arise from multiple independent mechanisms such as spati al, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles these influences by integrating mechanism - specific deep encoders with a structured Gaussian Process in a joint latent space. Disentanglement here refers to separating independently acting generative factors . The encoders isolate distinct mechanisms while the Gaussian Process captures their combined effect with calibrated uncertainty. The architecture supports structured priors, enabling interpretable and mechanism - aware prediction as well as efficient active l earning. Across benc hmarks, DIVIDE separates mechanisms, reproduces additive and scaled interactions, and remains robust under noise. The framework extends naturally to multifunctional datasets where mechanical, electromagnetic or optical responses coexist. INTRODUCTION Many real - world systems exhibit behavior driven by the combined influence of multiple independent mechanisms. These mechanisms may represent categorical factors, spatial dependencies, or nonlinear physical responses. While the scalar output of such systems is observable, the individual contributions of these mechanisms are often unknown and unmeasured. Modeling this type of data requires not only accurate predictions but also the ability to attribute variation in the output to specific, distinct sources. In thi s context, we use disentanglement to mean recovering those independently acting generative factors from observational data. Disentangling these contributions is particularly important in scientific and engineering domains where interpretability, causality, and mechanism - aware reasoning are essential. Partial solutions to this challenge have emerged from the field of disentangled representation learning, which seeks to identify independent factors of variation from high - dimensional data.