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This paper reviews the NTIRE 2022 Challenge on Super-Resolution and Quality Enhancement of Compressed Video. In this challenge, we proposed the LDV 2.0 dataset, which includes the LDV dataset (240 videos) and 95 additional videos. This challenge includes three tracks. Track 1 aims at enhancing the videos compressed by HEVC at a fixed QP. Track 2 and Track 3 target both the super-resolution and quality enhancement of HEVC compressed video. They require x2 and x4 super-resolution, respectively. The three tracks totally attract more than 600 registrations. In the test phase, 8 teams, 8 teams and 12 teams submitted the final results to Tracks 1, 2 and 3, respectively. The proposed methods and solutions gauge the state-of-the-art of super-resolution and quality enhancement of compressed video. The proposed LDV 2.0 dataset is available at https://github.com/RenYang-home/LDV_dataset. The homepage of this challenge (including open-sourced codes) is at https://github.com/RenYang-home/NTIRE22_VEnh_SR.

In this paper, we consider two challenging issues in reference-based super-resolution (RefSR), (i) how to choose a proper reference image, and (ii) how to learn real-world RefSR in a self-supervised manner. Particularly, we present a novel self-supervised learning approach for real-world image SR from observations at dual camera zooms (SelfDZSR). Considering the popularity of multiple cameras in modern smartphones, the more zoomed (telephoto) image can be naturally leveraged as the reference to guide the SR of the lesser zoomed (short-focus) image. Furthermore, SelfDZSR learns a deep network to obtain the SR result of short-focus image to have the same resolution as the telephoto image. For this purpose, we take the telephoto image instead of an additional high-resolution image as the supervision information and select a center patch from it as the reference to super-resolve the corresponding short-focus image patch. To mitigate the effect of the misalignment between short-focus low-resolution (LR) image and telephoto ground-truth (GT) image, we design an auxiliary-LR generator and map the GT to an auxiliary-LR while keeping the spatial position unchanged. Then the auxiliary-LR can be utilized to deform the LR features by the proposed adaptive spatial transformer networks (AdaSTN), and match the Ref features to GT. During testing, SelfDZSR can be directly deployed to super-solve the whole short-focus image with the reference of telephoto image. Experiments show that our method achieves better quantitative and qualitative performance against state-of-the-arts. Codes are available at https://github.com/cszhilu1998/SelfDZSR., Comment: ECCV 2022 camera ready

Image restoration problems are typical ill-posed problems where the regularization term plays an important role. The regularization term learned via generative approaches is easy to transfer to various image restoration, but offers inferior restoration quality compared with that learned via discriminative approaches. On the contrary, the regularization term learned via discriminative approaches are usually trained for a specific image restoration problem, and fail in the problem for which it is not trained. To address this issue, we propose a generic diffusion process (genericDP) to handle multiple Gaussian denoising problems based on the Trainable Non-linear Reaction Diffusion (TNRD) models. Instead of one model, which consists of a diffusion and a reaction term, for one Gaussian denoising problem in TNRD, we enforce multiple TNRD models to share one diffusion term. The trained genericDP model can provide both promising denoising performance and high training efficiency compared with the original TNRD models. We also transfer the trained diffusion term to non-blind deconvolution which is unseen in the training phase. Experiment results show that the trained diffusion term for multiple Gaussian denoising can be transferred to image non-blind deconvolution as an image prior and provide competitive performance., Comment: 12 pages, 3 figures, 3 tables

Compressive sensing (CS) has proved effective for tomographic reconstruction from sparsely collected data or under-sampled measurements, which are practically important for few-view CT, tomosynthesis, interior tomography, and so on. To perform sparse-data CT, the iterative reconstruction commonly use regularizers in the CS framework. Currently, how to choose the parameters adaptively for regularization is a major open problem. In this paper, inspired by the idea of machine learning especially deep learning, we unfold a state-of-the-art "fields of experts" based iterative reconstruction scheme up to a number of iterations for data-driven training, construct a Learned Experts' Assessment-based Reconstruction Network ("LEARN") for sparse-data CT, and demonstrate the feasibility and merits of our LEARN network. The experimental results with our proposed LEARN network produces a competitive performance with the well-known Mayo Clinic Low-Dose Challenge Dataset relative to several state-of-the-art methods, in terms of artifact reduction, feature preservation, and computational speed. This is consistent to our insight that because all the regularization terms and parameters used in the iterative reconstruction are now learned from the training data, our LEARN network utilizes application-oriented knowledge more effectively and recovers underlying images more favorably than competing algorithms. Also, the number of layers in the LEARN network is only 12, reducing the computational complexity of typical iterative algorithms by orders of magnitude., Comment: 18 pages, 15 figures, accepted by IEEE TMI

Speckle reduction is a prerequisite for many image processing tasks in synthetic aperture radar (SAR) images, as well as all coherent images. In recent years, predominant state-of-the-art approaches for despeckling are usually based on nonlocal methods which mainly concentrate on achieving utmost image restoration quality, with relatively low computational efficiency. Therefore, in this study we aim to propose an efficient despeckling model with both high computational efficiency and high recovery quality. To this end, we exploit a newly-developed trainable nonlinear reaction diffusion(TNRD) framework which has proven a simple and effective model for various image restoration problems. {In the original TNRD applications, the diffusion network is usually derived based on the direct gradient descent scheme. However, this approach will encounter some problem for the task of multiplicative noise reduction exploited in this study. To solve this problem, we employed a new architecture derived from the proximal gradient descent method.} {Taking into account the speckle noise statistics, the diffusion process for the despeckling task is derived. We then retrain all the model parameters in the presence of speckle noise. Finally, optimized nonlinear diffusion filtering models are obtained, which are specialized for despeckling with various noise levels. Experimental results substantiate that the trained filtering models provide comparable or even better results than state-of-the-art nonlocal approaches. Meanwhile, our proposed model merely contains convolution of linear filters with an image, which offers high level parallelism on GPUs. As a consequence, for images of size $512 \times 512$, our GPU implementation takes less than 0.1 seconds to produce state-of-the-art despeckling performance.}, Comment: to appear in Journal of Mathematical Imaging and Vision. Demo codes are available from https://1drv.ms/u/s!ApXF85Oq1kvqgcscP8GqUvPE-dF7ig

Image diffusion plays a fundamental role for the task of image denoising. Recently proposed trainable nonlinear reaction diffusion (TNRD) model defines a simple but very effective framework for image denoising. However, as the TNRD model is a local model, the diffusion behavior of which is purely controlled by information of local patches, it is prone to create artifacts in the homogenous regions and over-smooth highly textured regions, especially in the case of strong noise levels. Meanwhile, it is widely known that the non-local self-similarity (NSS) prior stands as an effective image prior for image denoising, which has been widely exploited in many non-local methods. In this work, we are highly motivated to embed the NSS prior into the TNRD model to tackle its weaknesses. In order to preserve the expected property that end-to-end training is available, we exploit the NSS prior by a set of non-local filters, and derive our proposed trainable non-local reaction diffusion (TNLRD) model for image denoising. Together with the local filters and influence functions, the non-local filters are learned by employing loss-specific training. The experimental results show that the trained TNLRD model produces visually plausible recovered images with more textures and less artifacts, compared to its local versions. Moreover, the trained TNLRD model can achieve strongly competitive performance to recent state-of-the-art image denoising methods in terms of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM)., Comment: under review in a journal

Image denoising is a fundamental operation in image processing and holds considerable practical importance for various real-world applications. Arguably several thousands of papers are dedicated to image denoising. In the past decade, sate-of-the-art denoising algorithm have been clearly dominated by non-local patch-based methods, which explicitly exploit patch self-similarity within image. However, in recent two years, discriminatively trained local approaches have started to outperform previous non-local models and have been attracting increasing attentions due to the additional advantage of computational efficiency. Successful approaches include cascade of shrinkage fields (CSF) and trainable nonlinear reaction diffusion (TNRD). These two methods are built on filter response of linear filters of small size using feed forward architectures. Due to the locality inherent in local approaches, the CSF and TNRD model become less effective when noise level is high and consequently introduces some noise artifacts. In order to overcome this problem, in this paper we introduce a multi-scale strategy. To be specific, we build on our newly-developed TNRD model, adopting the multi-scale pyramid image representation to devise a multi-scale nonlinear diffusion process. As expected, all the parameters in the proposed multi-scale diffusion model, including the filters and the influence functions across scales, are learned from training data through a loss based approach. Numerical results on Gaussian and Poisson denoising substantiate that the exploited multi-scale strategy can successfully boost the performance of the original TNRD model with single scale. As a consequence, the resulting multi-scale diffusion models can significantly suppress the typical incorrect features for those noisy images with heavy noise.

Poisson denoising is an essential issue for various imaging applications, such as night vision, medical imaging and microscopy. State-of-the-art approaches are clearly dominated by patch-based non-local methods in recent years. In this paper, we aim to propose a local Poisson denoising model with both structure simplicity and good performance. To this end, we consider a variational modeling to integrate the so-called Fields of Experts (FoE) image prior, that has proven an effective higher-order Markov Random Fields (MRF) model for many classic image restoration problems. We exploit several feasible variational variants for this task. We start with a direct modeling in the original image domain by taking into account the Poisson noise statistics, which performs generally well for the cases of high SNR. However, this strategy encounters problem in cases of low SNR. Then we turn to an alternative modeling strategy by using the Anscombe transform and Gaussian statistics derived data term. We retrain the FoE prior model directly in the transform domain. With the newly trained FoE model, we end up with a local variational model providing strongly competitive results against state-of-the-art non-local approaches, meanwhile bearing the property of simple structure. Furthermore, our proposed model comes along with an additional advantage, that the inference is very efficient as it is well-suited for parallel computation on GPUs. For images of size $512 \times 512$, our GPU implementation takes less than 1 second to produce state-of-the-art Poisson denoising performance., Comment: 31 pages, 10 figures. To appear in SIAM Journal on Imaging Sciences

Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise (AWGN) at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks such as Gaussian denoising, single image super-resolution and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this study we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly-developed trainable nonlinear reaction diffusion model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with an optimized nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on GPUs. For images of size $512 \times 512$, our GPU implementation takes less than 0.1 seconds to produce state-of-the-art Poisson denoising performance., Comment: 11 pages, 12 figures, technical report

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (\ie, linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD -- \textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast., Comment: 14 pages, 13 figures, to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI)

For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at the expense of very high computation time, which clearly limits their practical relevance. In this work, we propose a simple but effective approach with both high computational efficiency and high restoration quality. We extend conventional nonlinear reaction diffusion models by several parametrized linear filters as well as several parametrized influence functions. We propose to train the parameters of the filters and the influence functions through a loss based approach. Experiments show that our trained nonlinear reaction diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for image restoration. Due to their structural simplicity, our trained models are highly efficient and are also well-suited for parallel computation on GPUs., Comment: 9 pages, 3 figures, 3 tables. CVPR2015 oral presentation together with the supplemental material of 13 pages, 8 pages (Notes on diffusion networks)

A trainable filter-based higher-order Markov Random Fields (MRFs) model - the so called Fields of Experts (FoE), has proved a highly effective image prior model for many classic image restoration problems. Generally, two options are available to incorporate the learned FoE prior in the inference procedure: (1) sampling-based minimum mean square error (MMSE) estimate, and (2) energy minimization-based maximum a posteriori (MAP) estimate. This letter is devoted to the FoE prior based single image super resolution (SR) problem, and we suggest to make use of the MAP estimate for inference based on two facts: (I) It is well-known that the MAP inference has a remarkable advantage of high computational efficiency, while the sampling-based MMSE estimate is very time consuming. (II) Practical SR experiment results demonstrate that the MAP estimate works equally well compared to the MMSE estimate with exactly the same FoE prior model. Moreover, it can lead to even further improvements by incorporating our discriminatively trained FoE prior model. In summary, we hold that for higher-order natural image prior based SR problem, it is better to employ the MAP estimate for inference., Comment: 16 pages, 5 figures

The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this letter, we propose a novel variational model for multiplicative noise reduction based on the FoE image prior model. The resulted model corresponds to a non-convex minimization problem, which can be solved by a recently published non-convex optimization algorithm. Experimental results based on synthetic speckle noise and real synthetic aperture radar (SAR) images suggest that the performance of our proposed method is on par with the best published despeckling algorithm. Besides, our proposed model comes along with an additional advantage, that the inference is extremely efficient. {Our GPU based implementation takes less than 1s to produce state-of-the-art despeckling performance.}, Comment: 5 pages, 5 figures, to appear in IEEE Signal Processing Letters

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a non-smooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on non-convex problems. The convergence result is obtained based on the \KL inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and, then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems: image denoising with learned priors and diffusion based image compression., Comment: 32pages, 7 figures, to appear in SIAM Journal on Imaging Sciences

It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating existing training approaches, it turns out that the performance of the loss-specific training has been significantly underestimated in existing work. In this paper, we revisit this approach and use techniques from bi-level optimization to solve it. We show that we can get a substantial gain in the final performance by solving the lower-level problem in the bi-level framework with high accuracy using our newly proposed algorithm. As a result, our trained model is on par with highly specialized image denoising algorithms and clearly outperforms probabilistically trained MRF models. Our findings suggest that for the loss-specific training scheme, solving the lower-level problem with higher accuracy is beneficial. Our trained model comes along with the additional advantage, that inference is extremely efficient. Our GPU-based implementation takes less than 1s to produce state-of-the-art performance., Comment: 10 pages, 2 figures, appear at 35th German Conference, GCPR 2013, Saarbr\"ucken, Germany, September 3-6, 2013. Proceedings

We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is to learn a meaningful operator (dictionary) such that the minimum energy solution of the analysis (synthesis)-prior based model is as close as possible to the ground-truth. We solve the bi-level optimization problem using the implicit differentiation technique. Moreover, we demonstrate the effectiveness of our leaning approach by applying the learned analysis operator (dictionary) to the image denoising task and comparing its performance with state-of-the-art methods. Under this unified framework, we can compare the performance of the two types of priors., Comment: 5 pages, 1 figure, appear at the Workshop on Analysis Operator Learning vs. Dictionary Learning, NIPS 2012

Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of descriptive supporting points, which allow for an accurate reconstruction of the original image. It turns out in practice that this is a challenging problem even for the simplest Laplacian interpolation model. In this paper, we revisit the Laplacian interpolation compression model and introduce two fast algorithms, namely successive preconditioning primal dual algorithm and the recently proposed iPiano algorithm, to solve this problem efficiently. Furthermore, we extend the Laplacian interpolation based compression model to a more general form, which is based on principles from bi-level optimization. We investigate two different variants of the Laplacian model, namely biharmonic interpolation and smoothed Total Variation regularization. Our numerical results show that significant improvements can be obtained from the biharmonic interpolation model, and it can recover an image with very high quality from only 5% pixels., Comment: 8 pages, 4 figures, best paper award of CVWW 2014, Computer Vision Winter Workshop, K\v{r}tiny, Czech Republic, 3-5th February 2014

This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the Field of Experts (FoE) model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the analysis operators. Compared to existing analysis operator learning approaches, our training procedure has the advantage that it is unconstrained with respect to the analysis operator. We investigate the effect of different aspects of the co-sparse analysis model and show that the sparsity promoting function (also called penalty function) is the most important factor in the model. In order to demonstrate the effectiveness of our training approach, we apply our trained models to various classical image restoration problems. Numerical experiments show that our trained models clearly outperform existing analysis operator learning approaches and are on par with state-of-the-art image denoising algorithms. Our approach develops a framework that is intuitive to understand and easy to implement., Comment: 13 pages, 10 figures, accepted to IEEE Image Processing