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).
Fusing a low-resolution hyperspectral (HS) image with the corresponding high-resolution multispectral image to obtain a high-resolution HS image is an important technique for capturing comprehensive ...scene information in both the spatial and spectral domains. Existing approaches adopt sparsity promoting strategy and encode the spectral information of each pixel independently, which results in noisy sparse representation. We propose a novel HS image super-resolution method via a self-similarity constrained sparse representation. We explore the similar patch structures across the whole image and the pixels with close appearance in the local regions to create global-structure groups and local-spectral super-pixels. By forcing the similarity of the sparse representations for pixels belonging to the same group and super-pixel, we alleviate the effect of the outliers in the learned sparse coding. Experiment results on benchmark datasets validate that the proposed method outperforms the state-of-the-art methods in both the quantitative metrics and visual effect.
Let ð' be a prime. We say that a pro-ð' group is self-similar of index Image omitted if it admits a faithful self-similar action on a Image omitted -ary regular rooted tree such that the action ...is transitive on the first level. The self-similarity index of a self-similar pro-ð' group ðº is defined to be the least power of ð', say Image omitted, such that ðº is self-similar of index Image omitted. We show that, for every prime Image omitted and all integers ð'', there exist infinitely many pairwise non-isomorphic self-similar 3-dimensional hereditarily just-infinite uniform pro-ð' groups of self-similarity index greater than ð''. This implies that, in general, for self-similar ð'-adic analytic pro-ð' groups, one cannot bound the self-similarity index by a function that depends only on the dimension of the group.
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•A colorful superhydrophobic concrete (CSC) coating was developed.•The coating had good robustness due to high mechanical strength and self-similarity.•The coating possessed ...anti-icing, anti-corrosion and self-cleaning abilities.•The coating can be high-efficient and large-area fabricated.
Concrete is widely used in architecture because of its advantages such as high strength, low cost, good durability and plasticity. However, due to its hydrophilicity and porous structures, the concrete suffers from damages caused by oxidative corrosion, freezing environment, acid rain, etc. Superhydrophobic coating with excellent water-repellent property has great potential to solve this problem. However, a colorful and robust superhydrophobic coating which meets both performance and aesthetic requirements is still not reported. Here, we develop a colorful and robust superhydrophobic concrete (CSC) coating with a water contact angle of 158 ± 0.5° and a sliding angle of 5 ± 0.8° and composing of cement, sand, water-based stone protector, and dyes for concrete coloring. Four kinds of colors including red, yellow, blue, and green can be obtained by adding red, yellow, blue, and green iron oxide dyes, respectively. The high robustness is originated from the high adhesive force between the coating and the substrate, the inherent high hardness of concrete itself, and self-similarity of inside micro-structures. The CSC coating also exhibit excellent chemical durability and weather resistance. Thus, this kind of CSC coating has promising application prospects in the outside wall of concrete architecture to improve decorative and waterproof effects and keep clean.
Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity ...in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal patches with similar structures, and establish a novel sparse representation modeling of natural images, called group-based sparse representation (GSR). The proposed GSR is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. In addition, an effective self-adaptive dictionary learning method for each group with low complexity is designed, rather than dictionary learning from natural images. To make GSR tractable and robust, a split Bregman-based technique is developed to solve the proposed GSR-driven ℓ 0 minimization problem for image restoration efficiently. Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both peak signal-to-noise ratio and visual perception.
Through exploiting the image nonlocal self-similarity (NSS) prior by clustering similar patches to construct patch groups, recent studies have revealed that structural sparse representation (SSR) ...models can achieve promising performance in various image restoration tasks. However, most existing SSR methods only exploit the NSS prior from the input degraded (internal) image, and few methods utilize the NSS prior from external clean image corpus; how to jointly exploit the NSS priors of internal image and external clean image corpus is still an open problem. In this article, we propose a novel approach for image restoration by simultaneously considering internal and external nonlocal self-similarity (SNSS) priors that offer mutually complementary information. Specifically, we first group nonlocal similar patches from images of a training corpus. Then a group-based Gaussian mixture model (GMM) learning algorithm is applied to learn an external NSS prior. We exploit the SSR model by integrating the NSS priors of both internal and external image data. An alternating minimization with an adaptive parameter adjusting strategy is developed to solve the proposed SNSS-based image restoration problems, which makes the entire algorithm more stable and practical. Experimental results on three image restoration applications, namely image denoising, deblocking and deblurring, demonstrate that the proposed SNSS produces superior results compared to many popular or state-of-the-art methods in both objective and perceptual quality measurements.
In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. 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 observations, we progressively approximate 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. Towards 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 are updated gradually and jointly in each iteration. Based on the group-based sparse representation model, we further provide an analytical investigation on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC method outperforms many state-of-the-art schemes in both the objective and perceptual quality.
Group sparse representation (GSR) has made great strides in image restoration producing superior performance, realized through employing a powerful mechanism to integrate the local sparsity and ...nonlocal self-similarity of images. However, due to some form of degradation ( e.g. , noise, down-sampling or pixels missing), traditional GSR models may fail to faithfully estimate sparsity of each group in an image, thus resulting in a distorted reconstruction of the original image. This motivates us to design a simple yet effective model that aims to address the above mentioned problem. Specifically, we propose group sparsity residual constraint with nonlocal priors (GSRC-NLP) for image restoration. Through introducing the group sparsity residual constraint, the problem of image restoration is further defined and simplified through attempts at reducing the group sparsity residual. Towards this end, we first obtain a good estimation of the group sparse coefficient of each original image group by exploiting the image nonlocal self-similarity (NSS) prior along with self-supervised learning scheme, and then the group sparse coefficient of the corresponding degraded image group is enforced to approximate the estimation. To make the proposed scheme tractable and robust, two algorithms, i.e. , iterative shrinkage/thresholding (IST) and alternating direction method of multipliers (ADMM), are employed to solve the proposed optimization problems for different image restoration tasks. Experimental results on image denoising, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed GSRC-NLP based image restoration algorithm is comparable to state-of-the-art denoising methods and outperforms several testing image inpainting and image CS recovery methods in terms of both objective and perceptual quality metrics.
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