We study the complementary behaviors of external and internal examples in image restoration, and are motivated to formulate a composite dictionary design framework. The composite dictionary consists of the global part learned from external examples, and the sample-specific part learned from internal examples. The dictionary atoms in both parts are further adaptively weighted to emphasize their model statistics. Experiments demonstrate that the joint utilization of external and internal examples leads to substantial improvements, with successful applications in image denoising and super resolution.
Statistics of ‘natural images’ provides useful priors for solving under-constrained problems in Computer Vision. Such statistics is usually obtained from large collections of natural images. We claim that the substantial internal data redundancy within a single natural image (e.g., recurrence of small image patches), gives rise to powerful internal statistics, obtained directly from the image itself. While internal patch recurrence has been used in various applications, we provide a parametric quantification of this property. We show that the likelihood of an image patch to recur at another image location can be expressed parametricly as a function of the spatial distance from the patch, and its gradient content. This “internal parametric prior” is used to improve existing algorithms that rely on patch recurrence. Moreover, we show that internal image-specific statistics is often more powerful than general external statistics, giving rise to more powerful image-specific priors. In particular: (i) Patches tend to recur much more frequently (densely) inside the same image, than in any random external collection of natural images. (ii) To find an equally good external representative patch for all the patches of an image, requires an external database of hundreds of natural images. (iii) Internal statistics often has stronger predictive power than external statistics, indicating that it may potentially give rise to more powerful image-specific priors. Image denoising methods can broadly be classified into two types: “Internal Denoising” (denoising an image patch using other noisy patches within the noisy image), and “External Denoising” (denoising a patch using external clean natural image patches). Any such method, whether Internal or External, is typically applied to all image patches. In this paper we show that different image patches inherently have different preferences for Internal or External de-noising. Moreover, and surprisingly, the higher the noise in the image, the stronger the preference for Internal De-noising. We identify and explain the source of this behavior, and show that Internal External preference of a patch is directly related to its individual Signal-to-Noise-Ratio (“PatchSNR”). Patches with high PatchSNR (e.g., patches on strong edges) benefit much from External Denoising, whereas patches with low PatchSNR (e.g., patches in noisy uniform regions) benefit much more from Internal Denoising. Combining the power of Internal or External denoising selectively for each patch based on its estimated PatchSNR leads to improvement in denoising performance. Existing example-based super resolution (SR) methods are built upon either external-examples or self-examples. Although effective in certain cases, both methods suffer from their inherent limitation. This paper goes beyond these two classes of most common example-based SR approaches, and proposes a novel joint SR perspective. The joint SR exploits and maximizes the complementary advantages of external- and self-example based methods. We elaborate on exploitable priors for image components of different nature, and formulate their corresponding loss functions mathematically. Equipped with that, we construct a unified SR formulation, and propose an iterative joint super resolution (IJSR) algorithm to solve the optimization. Such a joint perspective approach leads to an impressive improvement of SR results both quantitatively and qualitatively. Deep learning has been successfully applied to image super resolution (SR). In this paper, we propose a deep joint super resolution (DJSR) model to exploit both external and self similarities for SR. A Stacked Denoising Convolutional Auto Encoder (SDCAE) is first pre-trained on external examples with proper data augmentations. It is then fine-tuned with multi-scale self examples from each input, where the reliability of self examples is explicitly taken into account. We also enhance the model performance by sub-model training and selection. The DJSR model is extensively evaluated and compared with state-of-the-arts, and show noticeable performance improvements both quantitatively and perceptually on a wide range of images. 