Group-based Sparse Representation Research Articles

Sparse-view CT reconstruction based on group-based sparse representation using weighted guided image filtering.

In the past, guided image filtering (GIF)-based methods often utilized total variation (TV)-based methods to reconstruct guidance images. And they failed to reconstruct the intricate details of complex clinical images accurately. Toaddress these problems, we propose a new sparse-view CT reconstruction method based on group-based sparse representation using weighted guided image filtering. In each iteration of the proposed algorithm, the result constrained by the group-based sparse representation (GSR) is used as the guidance image. Then, the weighted guided image filtering (WGIF) was used to transfer the important features from the guidance image to the reconstruction of the SART method. Three representative slices were tested under 64 projection views, and the proposed method yielded the best visual effect. For the shoulder case, the PSNR can achieve 48.82, which is far superior to other methods. The experimental results demonstrate that our method is more effective in preserving structures, suppressing noise, and reducing artifacts compared to other methods.

Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise

<abstract><p>In this article, we propose a novel group-based sparse representation (GSR) model for restoring color images in the presence of multiplicative noise. This model consists of a convex data-fidelity term, and two regularizations including GSR and saturation-value-based total variation (SVTV). The data-fidelity term is suitable for handling heavy multiplicative noise. GSR enables the retention of textures and details while sufficiently removing noise in smooth regions without producing the staircase artifacts engendered by total variation-based models. Furthermore, we introduce a multi-color channel-based GSR that involves coupling between three color channels. This avoids the generation of color artifacts caused by decoupled color channel-based methods. SVTV further improves the visual quality of restored images by diminishing certain artifacts induced by patch-based methods. To solve the proposed nonconvex model and its subproblem, we exploit the alternating direction method of multipliers, which contributes to an efficient iterative algorithm. Numerical results demonstrate the outstanding performance of the proposed model compared to other existing models regarding visual aspect and image quality evaluation values.</p></abstract>

Adaptive sparse modeling in spectral & spatial domain for compressed image restoration

Block discrete cosine transform (BDCT) is an indispensable component of modern image and video coding standards, specifically for its decorrelation and superior energy compaction aspects. BDCT typically employs block-specific quantization, which results in unpleasant compression-blocking artifacts which predominates at low bit rates. The proposed method aims to minimize these blocking artifacts to generate high-quality images under the framework of the alternating direction method of multipliers (ADMM) optimization. The proposed method exploits the local structures identified and extracted via wavelet-patch-based sparse representation and non-local self-similarity identified and extracted via group-based sparse representation, which are subsequently combined optimally employing ADMM. Moreover, the method uses a Gaussian quantization noise model, which allows a more precise and reliable assessment. An adaptive regularization parameter is used, which integrates spectral and spatial domain sparse representations with multi-resolution dictionaries and PCA-based dictionary. The proposed algorithm improves the overall practicality of the process and outperforms existing methods in terms of objective measures like structural similarity index measure, peak signal-to-noise ratio and visual perception.

ADMM optimizer for integrating wavelet-patch and group-based sparse representation for image inpainting

ADMM optimizer for integrating wavelet-patch and group-based sparse representation for image inpainting

Sparse angle CT reconstruction based on group sparse representation.

In order to solve the problem of image quality degradation of CT reconstruction under sparse angle projection, we propose to develop and test a new sparse angle CT reconstruction method based on group sparse. In this method, the group-based sparse representation is introduced into the statistical iterative reconstruction framework as a regularization term to construct the objective function. The group-based sparse representation no longer takes a single patch as the minimum unit of sparse representation, while it uses Euclidean distance as a similarity measure, thus it divides similar patch into groups as basic units for sparse representation. This method fully considers the local sparsity and non-local self-similarity of image. The proposed method is compared with several commonly used CT image reconstruction methods including FBP, SART, SART-TV and GSR-SART with experiments carried out on Sheep_Logan phantom and abdominal and pelvic images. In three experiments, the visual effect of the proposed method is the best. Under 64 projection angles, the lowest RMSE is 0.004776 and the highest VIF is 0.948724. FSIM and SSIM are all higher than 0.98. Under 50 projection angles, the index of the proposed method remains achieving the best image quality. Qualitative and quantitative results of this study demonstrate that this new proposed method can not only remove strip artifacts, but also effectively protect image details.

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints.

In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

A Hybrid Sparse Representation Model for Image Restoration.

Group-based sparse representation (GSR) uses image nonlocal self-similarity (NSS) prior to grouping similar image patches, and then performs sparse representation. However, the traditional GSR model restores the image by training degraded images, which leads to the inevitable over-fitting of the data in the training model, resulting in poor image restoration results. In this paper, we propose a new hybrid sparse representation model (HSR) for image restoration. The proposed HSR model is improved in two aspects. On the one hand, the proposed HSR model exploits the NSS priors of both degraded images and external image datasets, making the model complementary in feature space and the plane. On the other hand, we introduce a joint sparse representation model to make better use of local sparsity and NSS characteristics of the images. This joint model integrates the patch-based sparse representation (PSR) model and GSR model, while retaining the advantages of the GSR model and the PSR model, so that the sparse representation model is unified. Extensive experimental results show that the proposed hybrid model outperforms several existing image recovery algorithms in both objective and subjective evaluations.

Group-Based Sparse Representation for Compressed Sensing Image Reconstruction with Joint Regularization

Achieving high-quality reconstructions of images is the focus of research in image compressed sensing. Group sparse representation improves the quality of reconstructed images by exploiting the non-local similarity of images; however, block-matching and dictionary learning in the image group construction process leads to a long reconstruction time and artifacts in the reconstructed images. To solve the above problems, a joint regularized image reconstruction model based on group sparse representation (GSR-JR) is proposed. A group sparse coefficients regularization term ensures the sparsity of the group coefficients and reduces the complexity of the model. The group sparse residual regularization term introduces the prior information of the image to improve the quality of the reconstructed image. The alternating direction multiplier method and iterative thresholding algorithm are applied to solve the optimization problem. Simulation experiments confirm that the optimized GSR-JR model is superior to other advanced image reconstruction models in reconstructed image quality and visual effects. When the sensing rate is 0.1, compared to the group sparse residual constraint with a nonlocal prior (GSRC-NLR) model, the gain of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) is up to 4.86 dB and 0.1189, respectively.

Feature-guided dictionary learning for patch-and-group sparse representations in single image deraining

Single image deraining as a fundamental task in computer vision is important in improving the visual quality of images and videos. In this paper, we propose a feature-guided dictionary learning method for patch-and-group sparse representation in single image deraining. Specifically, we develop an external dictionary that learns the generic feature representation from a lot of natural images using Gaussian mixture models (GMMs), and a novel strategy is designed to learn an internal dictionary using the given rainy image guiding by the generic features. The external dictionary and the internal dictionary are adaptively tailored to produce a coherent dictionary, which can extend the representation abilities of the learned dictionary for the group-based sparse representation. Moreover, we present a novel patch-and-group sparse representation framework to reconstruct an image tending to be free of rain by simultaneously combining the local sparsity and the nonlocal self-similarity property. This framework can integrate their advantages of the two representative methods capable of capturing more effective features for the single image deraining. The results of experiments on both the synthetic and the real-world rainy images demonstrate that the proposed method delivers more favorable visual effects and superior quality results, and it outperforms several other state-of-the-art methods.

Single depth map super-resolution via joint non-local self-similarity modeling and local multi-directional gradient-guided regularization

The development of consumer depth cameras makes it possible to acquire depth information of a scene in real-time. However, low resolution and low quality of a depth map has greatly constrained its applications. In this paper, we propose a novel framework for single depth map super-resolution, which considers local and non-local information jointly in the depth map. For the non-local constraint, group-based sparse representation is used to explore non-local self-similarity in the depth map. For the local constraint, a multi-directional gradient-guided regularization is proposed to describe the gradient of the depth map with spatially varying orientations. The former constraint contains the visual artifacts effectively, while the latter restores sharp edge and fine structure. Finally, the two complementary regularizers are jointly casted into a unified optimization framework, where a split Bregman-based technique is developed to tackle the optimization problem. Both quantitative and qualitative evaluations indicate that the proposed method can obtain better reconstruction performance compared with state-of-the-art methods.

Group-Based Sparse Representation Based on lp-norm Minimization for Compressive Sensing

Group-Based Sparse Representation Based on lp-norm Minimization for Compressive Sensing

Image Restoration Using Joint Patch-Group-Based Sparse Representation

Sparse representation has achieved great success in various image processing and computer vision tasks. For image processing, typical patch-based sparse representation (PSR) models usually tend to generate undesirable visual artifacts, while group-based sparse representation (GSR) models lean to produce over-smooth effects. In this paper, we propose a new sparse representation model, termed joint patch-group based sparse representation (JPG-SR). Compared with existing sparse representation models, the proposed JPG-SR provides an effective mechanism to integrate the local sparsity and nonlocal self-similarity of images. We then apply the proposed JPG-SR to image restoration tasks, including image inpainting and image deblocking. An iterative algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed JPG-SR based image restoration problems. Experimental results demonstrate that the proposed JPG-SR is effective and outperforms many state-of-the-art methods in both objective and perceptual quality.

Group-Based Sparse Representation Based on lp -Norm Minimization for Image Inpainting

As a powerful statistical image modeling technique, sparse representation has been successfully applied in various image restoration applications. Most traditional methods depend on ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm optimization and patch-based sparse representation models. However, these methods have two limits: high computational complexity and the lack of the relationship among patches. To solve the above problems, we choose the group-based sparse representation models to simplify the computing process and realize the nonlocal self-similarity of images by designing the adaptive dictionary. Meanwhile, we utilize Ipnorm minimization to solve nonconvex optimization problems based on the weighted Schatten p-norm minimization, which can make the optimization model more flexible. Experimental results on image inpainting show that the proposed method has a better performance than many current state-of-the-art schemes, which are based on the pixel, patch, and group respectively, in both peak signal-to-noise ratio and visual perception.

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration.

In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observation, we progressively approximate (approach) the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Toward this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual qualities.

Single-image super-resolution via patch-based and group-based local smoothness modeling

Local smoothness and nonlocal self-similarity of natural images are two main priors in the image restoration (IR) problem. Many IR methods have widely used patch-based modeling. Recently, the concept of grouping-based technique, the nonlocal patches with similar structures, has been introduced as the basic unit of sparse representation. In the group-based methods, the nonlocal self-similarity and the local sparsity properties are combined in a unified framework using the sparsity-based techniques. In this paper, a new model is proposed which utilizes both the patch and the group as the basic units of image modeling, called patch-based and group-based local smoothness modeling (PGLSM). More, precisely, in the proposed PGLSM scheme, the local smoothness in the patch-based unit is exploited by an isotropic total variation method and the local smoothness in the group-based unit is exploited by group-based sparse representation method. In this way, a novel technique for high-fidelity single-image super-resolution (SISR) via PGLSM is proposed, called SR-PGLSM. By adding nonlocal means (NLM) as the complementary regularization term to PGLSM, another technique for SISR is modeled, called SR_PGLSM_NLM. In order to efficiently solve the above variational problems, the split Bergman iterative technique has been leveraged. Extensive experimental results validate the effectiveness and robustness of the proposed methods. Our proposed schemes can recover more fine structures and achieve better results than the competing methods with the scaling factor of 2 and 3 and for noisy images both subjectively and objectively in most cases.

An Effective Algorithm for Single Image Fog Removal

Poor visibility due to the effects of light absorption and scattering is challenging for processing images captured in foggy weather conditions. This paper proposes an effective algorithm for single image fog removal based on degradation model and group-based sparse representation (GSR). The proposed degradation model is constructed based on a classical physical model, i.e., dichromatic atmospheric scattering model. Then, the new degradation model is integrated into the group-based sparse representation framework. Finally, the single image defogging problem is regarded as an image restoration problem, which can be well optimized by GSR. The method is compared with several well-known algorithms from the literature using qualitative and quantitative evaluations, and results indicate considerable improvement over existing algorithms.

A new development of non-local image denoising using fixed-point iteration for non-convex ℓp sparse optimization.

We proposed a new efficient image denoising scheme, which mainly leads to four important contributions whose approaches are different from existing ones. The first is to show the equivalence between the group-based sparse representation and the Schatten-p norm minimization problem, so that the sparsity of the coefficients for each group can be measured by estimating the underlying singular values. The second is that we construct the proximal operator for sparse optimization in ℓp space with p ∈ (0, 1] by using fixed-point iteration and obtained a new solution of Schatten-p norm minimization problem, which is more rigorous and accurate than current available results. The third is that we analyze the suitable setting of power p for each noise level σ = 20, 30, 50, 60, 75, 100, respectively. We find that the optimal value of p is inversely proportional to the noise level except for high level of noise, where the best values of p are 1 and 0.95, when the noise levels are respectively 75 and 100. Last we measure the structural similarity between two image patches and extends previous deterministic annealing-based solution to sparsity optimization problem through incorporating the idea of dictionary learning. Experimental results demonstrate that for every given noise level, the proposed Spatially Adaptive Fixed Point Iteration (SAFPI) algorithm attains the best denoising performance on the value of Peak Signal-to-Noise Ratio (PSNR) and structure similarity (SSIM), being able to retain the image structure information, which outperforms many state-of-the-art denoising methods such as Block-matching and 3D filtering (BM3D), Weighted Nuclear Norm Minimization (WNNM) and Weighted Schatten p-Norm Minimization (WSNM).

ADMM for image restoration based on nonlocal simultaneous sparse Bayesian coding

Group-based sparse representation (GSR) models of natural images decompose each patch in group as a sparse linear combination from an over-complete dictionary and assume the sparse coefficients of each patch have a common set of nonzero support. Although the GSR models have shown great success in image restoration (IR) applications, however, current models are simple extension of traditional L0 or L1 sparse models and lack spatial adaption and principled fashion. In this paper, we propose a novel GSR model calling simultaneous sparse Bayesian coding (SSBC) model. In this model, the shared scaling variables in patch group are first learned by the empirical Bayesian strategy. Based on the learned scaling variables, the sparse coefficients can be efficiently solved by the posterior means of the coefficients. We further generalize this model to process general IR tasks with the alternating direction method of multipliers (ADMM) techniques. Extensive experiments on image denoising, inpainting, deblurring and single image super-resolution demonstrate that the proposed method achieves notable objective and subjective improvements over many state-of-the-art restored methods.

Simultaneous sparse coding with Laplacian scale mixture prior for image restoration

Group-based sparse representation modeling of natural images codes each patch in a group as a sparse linear combination from an over-complete dictionary and assumes that the coding coefficients of each patch have a common set of nonzero support. This model has shown great success in image restoration (IR) applications; however, current group-based sparse models are simple extensions of traditional L0 or L1 sparse models and lack spatial adaption and principled fashion. We propose a group-based sparse model named as simultaneously sparse coding with Laplacian scale mixture (LSM) prior through probabilistic approach. In this model, the representation coefficients of each patch in group are characterized by the same LSM prior, which is dominated by the shared scale variables. By imposing a hyperprior distribution over the scale variables, the sparse coefficients and shared scale variables can be jointly estimated via alternating optimization. Furthermore, we generalize this model to process more general IR problems under the plug-and-play alternating direction method of multipliers framework. Extensive experiments on image denoising, deblurring, and single-image super-resolution demonstrate that the proposed method achieves notable objective and subjective improvements over many state-of-the-art restored methods.

Group Sparsity based Sparse-Sampling CT Reconstruction.

Classical total variation (TV) based iterative re-construction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a novel computed tomography (CT) reconstruction method for the sparse-sampling problem called the group- sparsity regularization-based simultaneous algebraic reconstruction technique (GSR-SART). Group-based sparse representation, which utilizes the concept of a group as the basic unit of sparse representation instead of a patch, is introduced as the image domain prior regularization term to eliminate the over-smoothing effect. By grouping the nonlocal patches into different clusters with similarity measured by Euclidean distance, the sparsity and nonlocal similarity in a single image are simultaneously explored. The split Bregman iteration algorithm is applied to obtain the numerical scheme. Experimental results demonstrate that our method both qualitatively and quantitatively outperforms several existing reconstruction methods, including filtered back projection, expectation maximization, SART, and TV-based projections onto convex sets.