49865533
Learning Hybrid Sparsity Prior for Image Restoration: Where Deep Learning Meets Sparse Coding
State-of-the-art approaches toward image restoration can be classified into model-based and learning-based. The former - best represented by sparse coding techniques - strive to exploit intrinsic prior knowledge about the unknown high-resolution images; while the latter - popularized by recently developed deep learning techniques - leverage external image prior from some training dataset. It is natural to explore their middle ground and pursue a hybrid image prior capable of achieving the best in both worlds. In this paper, we propose a systematic approach of achieving this goal called Structured Analysis Sparse Coding (SASC). Specifically, a structured sparse prior is learned from extrinsic training data via a deep convolutional neural network (in a similar way to previous learning-based approaches); meantime another structured sparse prior is internally estimated from the input observation image (similar to previous model-based approaches). Two structured sparse priors will then be combined to produce a hybrid prior incorporating the knowledge from both domains. To manage the computational complexity, we have developed a novel framework of implementing hybrid structured sparse coding processes by deep convolutional neural networks. Experimental results show that the proposed hybrid image restoration method performs comparably with and often better than the current state-of-the-art techniques.
15091501
Image modeling and enhancement via structured sparse model selection
An image representation framework based on structured sparse model selection is introduced in this work. The corresponding modeling dictionary is comprised of a family of learned orthogonal bases. For an image patch, a model is first selected from this dictionary through linear approximation in a best basis, and the signal estimation is then calculated with the selected model. The model selection leads to a guaranteed near optimal denoising estimator. The degree of freedom in the model selection is equal to the number of the bases, typically about 10 for natural images, and is significantly lower than with traditional overcomplete dictionary approaches, stabilizing the representation. For an image patch of size √N × √N, the computational complexity of the proposed framework is O (N2), typically 2 to 3 orders of magnitude faster than estimation in an overcomplete dictionary. The orthogonal bases are adapted to the image of interest and are computed with a simple and fast procedure. State-of-the-art results are shown in image denoising, deblurring, and inpainting.
18943191
Single image super-resolution via BM3D sparse coding
In this paper, a novel single image super-resolution (SISR) algorithm is proposed. It is based on the BM3D (Block-Matching and 3D filtering) paradigm, where both sparsity and nonlocal patch self-similarity priors are utilized. The algorithm is derived from a variational formulation of the problem and has a structure typical for iterative back-projection super-resolution methods. They are characterized by updating high-resolution image which is calculated using the previous estimate and upsampled low-resolution error. The developed method is thoroughly compared with the state-of-the-art SISR both for noiseless and noisy data, demonstrating superior performance objectively and subjectively.
122523543
A wavelet tour of signal processing
Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.
7027533
Online dictionary learning for sparse coding
Sparse coding---that is, modelling data vectors as sparse linear combinations of basis elements---is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on learning the basis set, also called dictionary, to adapt it to specific data, an approach that has recently proven to be very effective for signal reconstruction and classification in the audio and image processing domains. This paper proposes a new online optimization algorithm for dictionary learning, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples. A proof of convergence is presented, along with experiments with natural images demonstrating that it leads to faster performance and better dictionaries than classical batch algorithms for both small and large datasets.
1475121
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.
14877173
Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
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.
6329825
Nonlocally Centralized Sparse Representation for Image Restoration
Sparse representation models code an image patch as a linear combination of a few atoms chosen out from an over-complete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred, and/or down-sampled), the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation-based image restoration, in this paper the concept of sparse coding noise is introduced, and the goal of image restoration turns to how to suppress the sparse coding noise. To this end, we exploit the image nonlocal self-similarity to obtain good estimates of the sparse coding coefficients of the original image, and then centralize the sparse coding coefficients of the observed image to those estimates. The so-called nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, while our extensive experiments on various types of image restoration problems, including denoising, deblurring and super-resolution, validate the generality and state-of-the-art performance of the proposed NCSR algorithm.
16118053
Image Restoration via Simultaneous Sparse Coding: Where Structured Sparsity Meets Gaussian Scale Mixture
In image processing, sparse coding has been known to be relevant to both variational and Bayesian approaches. The regularization parameter in variational image restoration is intrinsically connected with the shape parameter of sparse coefficients’ distribution in Bayesian methods. How to set those parameters in a principled yet spatially adaptive fashion turns out to be a challenging problem especially for the class of nonlocal image models. In this work, we propose a structured sparse coding framework to address this issue—more specifically, a nonlocal extension of Gaussian scale mixture (GSM) model is developed using simultaneous sparse coding (SSC) and its applications into image restoration are explored. It is shown that the variances of sparse coefficients (the field of scalar multipliers of Gaussians)—if treated as a latent variable—can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. When applied to image restoration, our experimental results have shown that the proposed SSC–GSM technique can both preserve the sharpness of edges and suppress undesirable artifacts. Thanks to its capability of achieving a better spatial adaptation, SSC–GSM based image restoration often delivers reconstructed images with higher subjective/objective qualities than other competing approaches.
6593498
Image Super-Resolution Using Deep Convolutional Networks
We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.
6594838
Deep Networks for Image Super-Resolution with Sparse Prior
Deep learning techniques have been successfully applied in many areas of computer vision, including low-level image restoration problems. For image super-resolution, several models based on deep neural networks have been recently proposed and attained superior performance that overshadows all previous handcrafted models. The question then arises whether large-capacity and data-driven models have become the dominant solution to the ill-posed super-resolution problem. In this paper, we argue that domain expertise represented by the conventional sparse coding model is still valuable, and it can be combined with the key ingredients of deep learning to achieve further improved results. We show that a sparse coding model particularly designed for super-resolution can be incarnated as a neural network, and trained in a cascaded structure from end to end. The interpretation of the network based on sparse coding leads to much more efficient and effective training, as well as a reduced model size. Our model is evaluated on a wide range of images, and shows clear advantage over existing state-of-the-art methods in terms of both restoration accuracy and human subjective quality.
206593506
Deeply-Recursive Convolutional Network for Image Super-Resolution
We propose an image super-resolution method (SR) using a deeply-recursive convolutional network (DRCN). Our network has a very deep recursive layer (up to 16 recursions). Increasing recursion depth can improve performance without introducing new parameters for additional convolutions. Albeit advantages, learning a DRCN is very hard with a standard gradient descent method due to exploding/ vanishing gradients. To ease the difficulty of training, we propose two extensions: recursive-supervision and skip-connection. Our method outperforms previous methods by a large margin.
13271756
Accelerating the Super-Resolution Convolutional Neural Network
As a successful deep model applied in image super-resolution (SR), the Super-Resolution Convolutional Neural Network (SRCNN) [1, 2] has demonstrated superior performance to the previous hand-crafted models either in speed and restoration quality. However, the high computational cost still hinders it from practical usage that demands real-time performance (24 fps). In this paper, we aim at accelerating the current SRCNN, and propose a compact hourglass-shape CNN structure for faster and better SR. We re-design the SRCNN structure mainly in three aspects. First, we introduce a deconvolution layer at the end of the network, then the mapping is learned directly from the original low-resolution image (without interpolation) to the high-resolution one. Second, we reformulate the mapping layer by shrinking the input feature dimension before mapping and expanding back afterwards. Third, we adopt smaller filter sizes but more mapping layers. The proposed model achieves a speed up of more than 40 times with even superior restoration quality. Further, we present the parameter settings that can achieve real-time performance on a generic CPU while still maintaining good performance. A corresponding transfer strategy is also proposed for fast training and testing across different upscaling factors.
7037846
Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network
Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods.
117543
Deep Network Cascade for Image Super-resolution
In this paper, we propose a new model called deep network cascade (DNC) to gradually upscale low-resolution images layer by layer, each layer with a small scale factor. DNC is a cascade of multiple stacked collaborative local auto-encoders. In each layer of the cascade, non-local self-similarity search is first performed to enhance high-frequency texture details of the partitioned patches in the input image. The enhanced image patches are then input into a collaborative local auto-encoder (CLA) to suppress the noises as well as collaborate the compatibility of the overlapping patches. By closing the loop on non-local self-similarity search and CLA in a cascade layer, we can refine the super-resolution result, which is further fed into next layer until the required image scale. Experiments on image super-resolution demonstrate that the proposed DNC can gradually upscale a low-resolution image with the increase of network layers and achieve more promising results in visual quality as well as quantitative performance.
9516233
Image Super-Resolution with Fast Approximate Convolutional Sparse Coding
We present a computationally efficient architecture for image super-resolution that achieves state-of-the-art results on images with large spatial extend. Apart from utilizing Convolutional Neural Networks, our approach leverages recent advances in fast approximate inference for sparse coding. We empirically show that upsampling methods work much better on latent representations than in the original spatial domain. Our experiments indicate that the proposed architecture can serve as a basis for additional future improvements in image super-resolution.
9971732
Accurate Image Super-Resolution Using Very Deep Convolutional Networks
We present a highly accurate single-image superresolution (SR) method. Our method uses a very deep convolutional network inspired by VGG-net used for ImageNet classification [19]. We find increasing our network depth shows a significant improvement in accuracy. Our final model uses 20 weight layers. By cascading small filters many times in a deep network structure, contextual information over large image regions is exploited in an efficient way. With very deep networks, however, convergence speed becomes a critical issue during training. We propose a simple yet effective training procedure. We learn residuals only and use extremely high learning rates (104 times higher than SRCNN [6]) enabled by adjustable gradient clipping. Our proposed method performs better than existing methods in accuracy and visual improvements in our results are easily noticeable.
15799108
Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration
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 (i.e., 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—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.
13333501
Learning Fast Approximations of Sparse Coding
In Sparse Coding (SC), input vectors are reconstructed using a sparse linear combination of basis vectors. SC has become a popular method for extracting features from data. For a given input, SC minimizes a quadratic reconstruction error with an L1 penalty term on the code. The process is often too slow for applications such as real-time pattern recognition. We proposed two versions of a very fast algorithm that produces approximate estimates of the sparse code that can be used to compute good visual features, or to initialize exact iterative algorithms. The main idea is to train a non-linear, feed-forward predictor with a specific architecture and a fixed depth to produce the best possible approximation of the sparse code. A version of the method, which can be seen as a trainable version of Li and Osher's coordinate descent method, is shown to produce approximate solutions with 10 times less computation than Li and Os-her's for the same approximation error. Unlike previous proposals for sparse code predictors, the system allows a kind of approximate "explaining away" to take place during inference. The resulting predictor is differentiable and can be included into globally-trained recognition systems.
2515179
The Cosparse Analysis Model and Algorithms
Abstract After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments, and provide a detailed study of the model associated with the 2D finite difference analysis operator, a close cousin of the TV norm.
7475296
Centralized sparse representation for image restoration
This paper proposes a novel sparse representation model called centralized sparse representation (CSR) for image restoration tasks. In order for faithful image reconstruction, it is expected that the sparse coding coefficients of the degraded image should be as close as possible to those of the unknown original image with the given dictionary. However, since the available data are the degraded (noisy, blurred and/or down-sampled) versions of the original image, the sparse coding coefficients are often not accurate enough if only the local sparsity of the image is considered, as in many existing sparse representation models. To make the sparse coding more accurate, a centralized sparsity constraint is introduced by exploiting the nonlocal image statistics. The local sparsity and the nonlocal sparsity constraints are unified into a variational framework for optimization. Extensive experiments on image restoration validated that our CSR model achieves convincing improvement over previous state-of-the-art methods.
996788
Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
The 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 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.
8187730
Image Super-Resolution Via Sparse Representation
This paper presents a new approach to single-image superresolution, based upon sparse signal representation. Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low-resolution and high-resolution image patch pair with respect to their own dictionaries. Therefore, the sparse representation of a low-resolution image patch can be applied with the high-resolution image patch dictionary to generate a high-resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs, compared to previous approaches, which simply sample a large amount of image patch pairs , reducing the computational cost substantially. The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution (SR) and the special case of face hallucination. In both cases, our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods. In addition, the local sparse modeling of our approach is naturally robust to noise, and therefore the proposed algorithm can handle SR with noisy inputs in a more unified framework.
1475121
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.
1726588
From learning models of natural image patches to whole image restoration
Learning good image priors is of utmost importance for the study of vision, computer vision and image processing applications. Learning priors and optimizing over whole images can lead to tremendous computational challenges. In contrast, when we work with small image patches, it is possible to learn priors and perform patch restoration very efficiently. This raises three questions - do priors that give high likelihood to the data also lead to good performance in restoration? Can we use such patch based priors to restore a full image? Can we learn better patch priors? In this work we answer these questions. We compare the likelihood of several patch models and show that priors that give high likelihood to data perform better in patch restoration. Motivated by this result, we propose a generic framework which allows for whole image restoration using any patch based prior for which a MAP (or approximate MAP) estimate can be calculated. We show how to derive an appropriate cost function, how to optimize it and how to use it to restore whole images. Finally, we present a generic, surprisingly simple Gaussian Mixture prior, learned from a set of natural images. When used with the proposed framework, this Gaussian Mixture Model outperforms all other generic prior methods for image denoising, deblurring and inpainting.
1663191
Weighted Nuclear Norm Minimization with Application to Image Denoising
As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
15799108
Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration
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 (i.e., 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—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.
18874645
Learning a Deep Convolutional Network for Image Super-Resolution
We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) [15] that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage.
206593506
Deeply-Recursive Convolutional Network for Image Super-Resolution
We propose an image super-resolution method (SR) using a deeply-recursive convolutional network (DRCN). Our network has a very deep recursive layer (up to 16 recursions). Increasing recursion depth can improve performance without introducing new parameters for additional convolutions. Albeit advantages, learning a DRCN is very hard with a standard gradient descent method due to exploding/ vanishing gradients. To ease the difficulty of training, we propose two extensions: recursive-supervision and skip-connection. Our method outperforms previous methods by a large margin.