Weisheng Dong

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.

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.

Sparsity-based image denoising via dictionary learning and structural clustering

Where does the sparsity in image signals come from? Local and nonlocal image models have supplied complementary views toward the regularity in natural images — the former attempts to construct or learn a dictionary of basis functions that promotes the sparsity; while the latter connects the sparsity with the self-similarity of the image source by clustering. In this paper, we present a variational framework for unifying the above two views and propose a new denoising algorithm built upon clustering-based sparse representation (CSR). Inspired by the success of l1-optimization, we have formulated a double-header l1-optimization problem where the regularization involves both dictionary learning and structural structuring. A surrogate-function based iterative shrinkage solution has been developed to solve the double-header l1-optimization problem and a probabilistic interpretation of CSR model is also included. Our experimental results have shown convincing improvements over state-of-the-art denoising technique BM3D on the class of regular texture images. The PSNR performance of CSR denoising is at least comparable and often superior to other competing schemes including BM3D on a collection of 12 generic natural images.

Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach

Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of natural images. Meanwhile, the problem of sparsity optimization, especially when tangled with dictionary learning, is computationally difficult to solve. In this paper, we take a low-rank approach toward SSC and provide a conceptually simple interpretation from a bilateral variance estimation perspective, namely that singular-value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances. Such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular-value thresholding (SAIST). For noise data, SAIST generalizes the celebrated BayesShrink from local to nonlocal models; for incomplete data, SAIST extends previous deterministic annealing-based solution to sparsity optimization through incorporating the idea of dictionary learning. In addition to conceptual simplicity and computational efficiency, SAIST has achieved highly competent (often better) objective performance compared to several state-of-the-art methods in image denoising and completion experiments. Our subjective quality results compare favorably with those obtained by existing techniques, especially at high noise levels and with a large amount of missing data.

Sparse Representation Based Image Interpolation With Nonlocal Autoregressive Modeling

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.

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.

Compressive sensing via nonlocal low-rank regularization.

Sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements. Recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing (CS) studies. In this paper, we propose a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its application into CS of both photographic and MRI images. We also propose the use of a nonconvex log det ( X) as a smooth surrogate function for the rank instead of the convex nuclear norm and justify the benefit of such a strategy using extensive experiments. To further improve the computational efficiency of the proposed algorithm, we have developed a fast implementation using the alternative direction multiplier method technique. Experimental results have shown that the proposed NLR-CS algorithm can significantly outperform existing state-of-the-art CS techniques for image recovery.

Nonlocal back-projection for adaptive image enlargement

This paper presents a novel non-local iterative back-projection (NLIBP) algorithm for image enlargement. The iterative back-projection (IBP) technique iteratively reconstructs a high resolution (HR) image from its blurred and downsampled low resolution (LR) counterpart. However, the conventional IBP methods often produce many “jaggy” and “ringing” artifacts because the reconstruction errors are back projected into the reconstructed image isotropically and locally. In natural images, usually there exist many non-local redundancies which can be exploited to improve the image reconstruction quality. Therefore, we propose to incorporate adaptively the non-local information into the IBP process so that the reconstruction errors can be reduced. Experimental results demonstrated that the proposed NLBP can reconstruct faithfully the HR images with sharp edges and texture structures. It outperforms the state-of-the-art methods in both PSNR and visual perception.

Image reconstruction with locally adaptive sparsity and nonlocal robust regularization

Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment.

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.