Super-resolution (SR) is a technique that allows increasing the resolution of a given image. Having applications in many areas, from medical imaging to consumer electronics, several SR methods have been proposed. Currently, the best performing methods are based on convolutional neural networks (CNNs) and require extensive datasets for training. However, at test time, they fail to impose consistency between the super-resolved image and the given low-resolution image, a property that classic reconstruction-based algorithms naturally enforce in spite of having poorer performance. Motivated by this observation, we propose a new framework that joins both approaches and produces images with superior quality than any of the prior methods. Although our framework requires additional computation, our experiments on Set5, Set14, and BSD100 show that it systematically produces images with better peak signal to noise ratio (PSNR) and structural similarity (SSIM) than the current state-of-the-art CNN architectures for SR.
Alternative regularizers Natural images also have simple representations in other domains, and other regularizers have been used for SR. For example, @cite_18 uses the fact that images have sparse wavelet representations. The patches of natural images also tend to lie on a low-dimensional manifold @cite_13 , which has motivated nonlocal methods. These use as regularizers (nonconvex) functions that enforce many patches of an image to have similar features; see, e.g., @cite_2 @cite_41 . Finally, different regularizers can be combined as in @cite_3 @cite_19 .
@cite_18 @cite_41 @cite_3 @cite_19 @cite_2 @cite_13
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Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences. Image super-resolution (SR) aims to recover high-resolution images from their low-resolution counterparts for improving image analysis and visualization. Interpolation methods, widely used for this purpose, often result in images with blurred edges and blocking effects. More advanced methods such as total variation (TV) retain edge sharpness during image recovery. However, these methods only utilize information from local neighborhoods, neglecting useful information from remote voxels. In this paper, we propose a novel image SR method that integrates both local and global information for effective image recovery. This is achieved by, in addition to TV, low-rank regularization that enables utilization of information throughout the image. The optimization problem can be solved effectively via alternating direction method of multipliers (ADMM). Experiments on MR images of both adult and pediatric subjects demonstrate that the proposed method enhances the details in the recovered high-resolution images, and outperforms methods such as the nearest-neighbor interpolation, cubic interpolation, iterative back projection (IBP), non-local means (NLM), and TV-based up-sampling. It is difficult to design an image super-resolution algorithm that can not only preserve image edges and texture structure but also keep lower computational complexity. A new super-resolution model based on sparsity regularization in Bayesian framework is presented. The fidelity term restricts the underlying image to be consistent with the observation image in terms of the image degradation model. The sparsity regularization term constraints the underlying image with a sparse representation in a proper dictionary. The non-local self-similarity is also introduced into the model. In order to make the sparse domain better represent the underlying image, we use high-frequency features extracted from the underlying image patches for sparse representation, which increases the effectiveness of sparse modeling. The proposed method learns dictionary directly from the estimated high-resolution image patches (extracted features), and the dictionary learning and the super-resolution can be fused together naturally into one coherent and iterated process. Such a self-learning method has stronger adaptability to different images and reduces dictionary training time. Experiments demonstrate the effectiveness of the proposed method. Compared with some state-of-the-art methods, the proposed method can better preserve image edges and texture details. This article proposes a new framework to regularize linear inverse problems using the total variation on non-local graphs. This non-local graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regularization process and the non-local graph adapted to this solution. We show numerical applications of this method to the resolution of image processing inverse problems such as inpainting, super-resolution and compressive sampling. Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.