Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast ($\sim 0.08$ s for a $128\times 128$ image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

Super-resolution (SR) from a single image plays an important role in many computer vision applications. It aims to estimate a high-resolution (HR) image from an input low- resolution (LR) image. To ensure a reliable and robust estimation of the HR image, we propose a novel single image SR method that exploits both the local geometric duality (GD) and the non-local similarity of images. The main principle is to formulate these two typically existing features of images as effective priors to constrain the super-resolved results. In consideration of this principle, the robust soft-decision interpolation method is generalized as an outstanding adaptive GD (AGD)-based local prior. To adaptively design weights for the AGD prior, a local non-smoothness detection method and a directional standard-deviation-based weights selection method are proposed. After that, the AGD prior is combined with a variational-framework-based non-local prior. Furthermore, the proposed algorithm is speeded up by a fast GD matrices construction method, which primarily relies on the selective pixel processing. The extensive experimental results verify the effectiveness of the proposed method compared with several state-of-the-art SR algorithms.

Deep learning methods have shown remarkable performance in image denoising, particularly when trained on large-scale paired datasets. However, acquiring such paired datasets for real-world scenarios poses a significant challenge. Although unsupervised approaches based on generative adversarial networks (GANs) offer a promising solution for denoising without paired datasets, they are difficult in surpassing the performance limitations of conventional GAN-based unsupervised frameworks without significantly modifying existing structures or increasing the computational complexity of denoisers. To address this problem, we propose a self-collaboration (SC) strategy for multiple denoisers. This strategy can achieve significant performance improvement without increasing the inference complexity of the GAN-based denoising framework. Its basic idea is to iteratively replace the previous less powerful denoiser in the filter-guided noise extraction module with the current powerful denoiser. This process generates better synthetic clean-noisy image pairs, leading to a more powerful denoiser for the next iteration. In addition, we propose a baseline method that includes parallel generative adversarial branches with complementary "self-synthesis" and "unpaired-synthesis" constraints. This baseline ensures the stability and effectiveness of the training network. The experimental results demonstrate the superiority of our method over state-of-the-art unsupervised methods. https://github.com/linxin0/SCPGabNet

Deep learning-based methods have dominated the field of image denoising with their superior performance. Most of them belong to the non-blind denoising approaches assuming that the noise is known at a specific level. However, real-world noise is complex and usually unknown. Since the distribution and level of noise are often unavailable, it will lead to severe performance degradation for non-blind denoising methods. Therefore, introducing noise levels is crucial for the challenging real-world denoising problem. Meanwhile, we observe that noise level mismatch will bring some artifacts to the denoised images. An intuitive solution is using the intermediate denoised images to correct the inaccurate noise level maps. Thus, we introduce an iterative correction scheme, yielding better results than direct noise prediction. We further propose an effective guided feature domain denoising residual network that can promote denoising for various real-world noises using iteratively denoised features, initial image features, and noise level maps. Experimental results on real-world image datasets show that the proposed method can provide excellent visual and objective performance for the real-world denoising task.

Image restoration (IR) problems are very important in many low-level vision tasks. Due to their ill-posed natures, image priors are widely used to regularize the solution spaces. Recently, patch-based non-local self-similarity has shown great potential in IR problems, leading to many effective non-local priors. Their performance largely depends on whether the non-local self-similarity of the underlying image can be fully exploited. However, most of these priors, including non-local regression (NLR), only utilize the center pixel of each patch to model the non-local feature, which is suboptimal. We propose an effective overlap-based non-local regression (ONLR) to fully exploit the non-local similar patches: first, the concept of overlap-based similar pixels group (OSPG) is introduced; second, for each pixel within an OSPG, the non-local weight is obtained via a novel similarity measurement method; third, based on the consistency assumption, the non-local fitting deviations (NLFDs) by using OSPGs are uniformly constrained. Because of the uniform constraints, the restoration may be poor in regions where OSPGs are not reliable. Consequently, a weighting scheme is proposed to measure the OSPG reliability, leading to a novel adjusted non-local regression (ANLR). In addition, the integral image technique (IIT) is adopted to speed up the similar patches search process. To further boost the ANLR, a local directional smoothness (DS) prior is proposed as a good complement of the non-local feature. Finally, a fast split Bregman iteration algorithm is designed to solve the ANLR-DS minimization problem. Extensive experiments on two typical IR problems, that is, image deblurring and super resolution, demonstrate the superiority of the proposed method compared to many state-of-the-art IR methods.