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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Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM. As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of the l1-norm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a precollected dataset of example image patches, and then, for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image nonlocal self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception. Example learning-based image super-resolution (SR) is recognized as an effective way to produce a high-resolution (HR) image with the help of an external training set. The effectiveness of learning-based SR methods, however, depends highly upon the consistency between the supporting training set and low-resolution (LR) images to be handled. To reduce the adverse effect brought by incompatible high-frequency details in the training set, we propose a single image SR approach by learning multiscale self-similarities from an LR image itself. The proposed SR approach is based upon an observation that small patches in natural images tend to redundantly repeat themselves many times both within the same scale and across different scales. To synthesize the missing details, we establish the HR-LR patch pairs using the initial LR input and its down-sampled version to capture the similarities across different scales and utilize the neighbor embedding algorithm to estimate the relationship between the LR and HR image pairs. To fully exploit the similarities across various scales inside the input LR image, we accumulate the previous resultant images as training examples for the subsequent reconstruction processes and adopt a gradual magnification scheme to upscale the LR input to the desired size step by step. In addition, to preserve sharper edges and suppress aliasing artifacts, we further apply the nonlocal means method to learn the similarity within the same scale and formulate a nonlocal prior regularization term to well pose SR estimation under a reconstruction-based SR framework. Experimental results demonstrate that the proposed method can produce compelling SR recovery both quantitatively and perceptually in comparison with other state-of-the-art baselines. Patch based image modeling has achieved a great success in low level vision such as image denoising. In particular, the use of image nonlocal self-similarity (NSS) prior, which refers to the fact that a local patch often has many nonlocal similar patches to it across the image, has significantly enhanced the denoising performance. However, in most existing methods only the NSS of input degraded image is exploited, while how to utilize the NSS of clean natural images is still an open problem. In this paper, we propose a patch group (PG) based NSS prior learning scheme to learn explicit NSS models from natural images for high performance denoising. PGs are extracted from training images by putting nonlocal similar patches into groups, and a PG based Gaussian Mixture Model (PG-GMM) learning algorithm is developed to learn the NSS prior. We demonstrate that, owe to the learned PG-GMM, a simple weighted sparse coding model, which has a closed-form solution, can be used to perform image denoising effectively, resulting in high PSNR measure, fast speed, and particularly the best visual quality among all competing methods.