Recent advancements have suggested that neural radiance fields (NeRFs) show great potential in color editing within the 3D domain. However, most existing NeRF-based editing methods continue to face significant challenges in local region editing, which usually lead to imprecise local object boundaries, difficulties in maintaining multi-view consistency, and over-reliance on annotated data. To address these limitations, in this paper, we propose a novel weakly-supervised method called KaRF for local color editing, which facilitates high-fidelity and realistic appearance edits in arbitrary regions of 3D scenes. At the core of the proposed KaRF approach is a unified two-stage Kolmogorov-Arnold Networks (KANs)-based radiance fields framework, comprising a segmentation stage followed by a local recoloring stage. This architecture seamlessly integrates geometric priors from NeRF to achieve weakly-supervised learning, leading to superior performance. More specifically, we propose a residual adaptive gating KAN structure, which integrates KAN with residual connections, adaptive parameters, and gating mechanisms to effectively enhance segmentation accuracy and refine specific editing effects. Additionally, we propose a palette-adaptive reconstruction loss, which can enhance the accuracy of additive mixing results. Extensive experiments demonstrate that the proposed KaRF algorithm significantly outperforms many state-of-the-art methods both qualitatively and quantitatively. Our code and more results are available at: https://github.com/PaiDii/KARF.git.

Deep neural networks (DNNs) are potent in LiDAR-based 3D object detection (LiDAR-3DOD), yet their deployment remains daunting due to their cumbersome parameters and computations. Knowledge distillation (KD) is promising for compressing DNNs in LiDAR-3DOD. However, most existing KD methods transfer inadequate knowledge between homogeneous detectors, and do not thoroughly explore optimal student architectures, resulting in insufficient gains for compact student detectors. To this end, we propose a category knowledge-driven compression framework to achieve efficient LiDAR-based 3D detectors. Firstly, we distill knowledge from two-stage teacher detectors to one-stage student detectors, overcoming the limitations of homogeneous pairs. To conduct KD in these heterogeneous pairs, we explore the gap between heterogeneous detectors, and introduce category knowledge-driven KD (CaKD), which includes both student-oriented distillation and two-stage-oriented label assignment distillation. Secondly, to search for the optimal architecture of compact student detectors, we introduce a masked category knowledge-driven structured pruning scheme. This scheme evaluates filter importance by analyzing the changes in category predictions related to foreground regions before and after filter removal, and prunes the less important filters accordingly. Finally, we propose a modified IoU-aware redundancy elimination module to remove redundant false positive samples, thereby further improving the accuracy of detectors. Experiments on various point cloud datasets demonstrate that our method delivers impressive results. For example, on KITTI, several compressed one-stage detectors outperform two-stage detectors in both efficiency and accuracy. Besides, on WOD-mini, our framework reduces the memory footprint of CenterPoint by 5.2× and improves the L2 mAPH by 0.55$\%$%.

Recent advancements have suggested that neural radiance fields (NeRFs) show great potential in 3D style transfer. However, most existing NeRF-based style transfer methods still face considerable challenges in generating stylized images that simultaneously preserve clear scene textures and maintain strong cross-view consistency. To address these limitations, in this paper, we propose a novel transformer-guided approach for 3D scene style transfer. Specifically, we first design a transformer-based style transfer network to capture long-range dependencies and generate 2D stylized images with initial consistency, which serve as supervision for the 3D stylized generation. To enable fine-grained control over style, we propose a latent style vector as a conditional feature and design a style network that projects this style information into the 3D space. We further develop a merge network that integrates style features with scene geometry to render 3D stylized images that are both visually coherent and stylistically consistent. In addition, we propose a texture consistency loss to preserve scene structure and enhance texture fidelity across views. Extensive quantitative and qualitative experimental results demonstrate that our proposed approach outperforms many state-of-the-art methods in terms of visual perception, image quality and multi-view consistency. Our code and more results are available at: https://github.com/PaiDii/TGTC-Style.git.

Knowledge Graph (KG) have attained notable triumph over Question Answering (QA) tasks. However, the presence of temporal constraints on numerous facts within the real world has sparked heightened interest towards Temporal KGQA (TKGQA). Although previous methods have achieved great progress, they still have the following limitations: 1)PLMs cannot capture the entity drift caused by time constraints in the question. 2) Complex questions require multi-hop reasoning between entities. 3) Fusion strategies (addition or concatenation) of PLMs and KG information ignore feature differences, resulting in suboptimal solutions. To alleviate the above problems, we propose a novel Multi-view, Multi-hop and Multi-stage reasoning paradigm for TKGQA (M3TQA). Specifically, we first design a multi-view calibration module for fusing KG information to calibrate question representation. We next construct graph neural network in a multi-hop modeling module to capture multi-hop message passing between entities. Finally, we design multi-stage aggregation that facilitates the adaptive fusion of heterogeneous information with a two-stage interaction alignment process. The performance on two mainstream benchmark datasets verifies the effectiveness of our proposed model.

Recently, Grounded Multimodal Named Entity Recognition (GM-NER) task has been introduced to refine the Multimodal Named Entity Recognition (MNER) task.Existing MNER studies fall short in that they merely focus on extracting text-based entity-type pairs, often leading to entity ambiguities and failing to contribute to multimodal knowledge graph construction.In the GMNER task, the objective becomes more challenging: identifying named entities in text, determining their entity types, and locating their corresponding bounding boxes in linked images, necessitating precise alignment between the textual and visual information.We introduce a novel multi-level alignment pre-training method, engaging with both text-image and entity-object dimensions to foster deeper congruence between multimodal data.Specifically, we innovatively harness potential objects identified within images, aligning them with textual entity prompts, thereby generating refined soft pseudolabels.These labels serve as self-supervised signals that pre-train the model to more accurately extract entities from textual input.To address misalignments that often plague modality integration, our method employs a sophisticated diffusion model that performs back-translation on the text to generate a corresponding visual representation, thus refining the model's multimodal interpretative accuracy.Empirical evidence from the GMNER dataset validates that our approach significantly outperforms existing state-of-theart models.Moreover, the versatility of our pre-training process complements virtually all extant models, offering an additional avenue for augmenting their multimodal entity recognition acumen.

Low-rank matrix recovery is a major challenge in machine learning and computer vision, particularly for large-scale data matrices, as popular methods involving nuclear norm and singular value decomposition (SVD) are associated with high computational costs and biased estimators. To overcome this challenge, we propose a novel approach to learning low-rank matrices based on the matrix volume and a nonconvex logarithmic function. The matrix volume is the product of all the nonzero singular values of a matrix and has unique geometric properties and connections with other convex and nonconvex functions. We establish a generalized nonconvex regularization problem using the penalty function strategy and introduce an accelerated proximal alternating linearized minimization (AccPALM) algorithm with double acceleration, which combines Nesterov’s acceleration and power strategy. The algorithm reduces computational costs and has provable convergence results under the Kurdyka-Łojasiewicz (KŁ) inequality with mild conditions. Our approach shows superior accuracy, efficiency, and convergence behavior compared to other low-rank matrix learning methods on robust matrix completion (RMC) and low-rank representation (LRR) tasks. We analyze the impact of algorithm parameters on convergence and performance and present visually appealing results to further demonstrate the effectiveness of our approach. The proposed methodology represents a promising advance in the field of low-rank matrix recovery, and its effectiveness has been validated via extensive numerical experiments. The source code for the proposed algorithms is accessible at https://github.com/ZhangHengMin/AccPALMcodes.

Compressive sensing (CS) techniques using a few compressed measurements have drawn considerable interest in reconstructing multispectral imagery (MSI). Nonlocal-based tensor methods have been widely used for MSI-CS reconstruction, which employ the nonlocal self-similarity (NSS) property of MSI to obtain satisfactory results. However, such methods only consider the internal priors of MSI while ignoring important external image information, for example deep-driven priors learned from a corpus of natural image datasets. Meanwhile, they usually suffer from annoying ringing artifacts due to the aggregation of overlapping patches. In this article, we propose a novel approach for highly effective MSI-CS reconstruction using multiple complementary priors (MCPs). The proposed MCP jointly exploits nonlocal low-rank and deep image priors under a hybrid plug-and-play framework, which contains multiple pairs of complementary priors, namely, internal and external, shallow and deep, and NSS and local spatial priors. To make the optimization tractable, a well-known alternating direction method of multiplier (ADMM) algorithm based on the alternating minimization framework is developed to solve the proposed MCP-based MSI-CS reconstruction problem. Extensive experimental results demonstrate that the proposed MCP algorithm outperforms many state-of-the-art CS techniques in MSI reconstruction. The source code of the proposed MCP-based MSI-CS reconstruction algorithm is available at: https://github.com/zhazhiyuan/MCP_MSI_CS_Demo.git.

In real-world applications involving sparse coding and low-rank matrix recovery problems, linear regression methods usually struggle to effectively capture the structured correlations present in data matrices. This limitation arises from representation approaches that treat images as vectors and handle testing samples individually, overlooking these correlations. To address these challenges, we propose a novel approach that leverages the low-rank property to capture the global and intrinsic structure of residual and coefficient matrices, departing from the assumption of independent and identically distributed (I.I.D) data. Our method introduces nonconvex and nonsmooth low-rank matrix regression models guided by the extended matrix variate power exponential distribution (M.P.E.D). By incorporating factorization strategies into the regression coefficient matrix and utilizing the Schatten-$p$norm with three distinct values of$p$, we enhance computational efficiency. Our formulation enables efficient subproblem solving through the introduction of auxiliary variables and the use of singular value threshold operators. We achieve closed-form solutions using the proposed multi-variable alternating direction method of multipliers (ADMM). Theoretical analysis establishes the local convergence properties and computational complexity of our optimization algorithm. Furthermore, we conduct numerical experiments on various image datasets, including face, object, and digital, to demonstrate the superior performance and computational efficiency of our methods compared to several related regression approaches. The source codes for our method are available athttps://github.com/ZhangHengMin/TIFS_SLRMFR.

Multimodal named entity recognition (MNER) is a vision-language task, which aims to detect entity spans and classify them to corresponding entity types given a sentence-image pair. Existing methods often regard an image as a set of visual objects, trying to explicitly capture the relations between visual objects and entities. However, since visual objects are often not identical to entities in quantity and type, they may suffer the bias introduced by visual objects rather than aid. Inspired by the success of textual prompt-based fine-tuning (PF) approaches in many methods, in this paper, we propose a Multimodal Prompt-based Machine Reading Comprehension based framework to implicit alignment between text and image for improving MNER, namely MPMRC-MNER. Specifically, we transform text-only query in MRC into multimodal prompt containing image tokens and text tokens. To better integrate image tokens and text tokens, we design a prompt-aware attention mechanism for better cross-modal fusion. At last, contrastive learning with two types of contrastive losses is designed to learn more consistent representation of two modalities and reduce noise. Extensive experiments and analyses on two public MNER datasets, Twitter2015 and Twitter2017, demonstrate the better performance of our model against the state-of-the-art methods.

Nonlocal low-rank (LR) tensor modeling has shown great potential in hyperspectral image (HSI) denoising, which first uses the nonlocal self-similarity (NSS) prior to search for many similar full-band patches to form three-dimensional nonlocal full-band groups (tensors), and then usually enforces an LR penalty on each nonlocal full-band group. However, in most existing methods, the LR tensor is only approximated directly from the degraded nonlocal full-band tensor, which is subject to certain issues (e.g., in heavy noise environments) in obtaining a suboptimal tensor approximation, and thus leading to unsatisfactory denoising results. In this paper, we propose a novel nonlocal rank residual (NRR) approach for highly effective HSI denoising, which progressively approximates the underlying L-R tensor via minimizing the rank residual. Towards this end, we first obtain a good estimate of the original nonlocal full-band group by using the NSS prior, and then the rank residual between the de-graded nonlocal full-band group with the corresponding estimated nonlocal full-band group is minimized to achieve a more accurate LR tensor. Moreover, the global spectral LR prior is employed to reduce the spectral redundancy of HSI in the proposed denoising framework. Finally, we develop a simple yet effective alternating minimization algorithm to jointly refine global spectral information and nonlocal full-band groups. Experimental results clearly show that the proposed NRR algorithm outperforms many state-of-the-art HSI denoising methods. The source code of the proposed NRR algorithm for HSI denoising is available at: https://github.com/zhazhiyuan/NRR_HSI_Denoising_Demo.git.

With the growing interest in convex and nonconvex low-rank matrix learning problems, the widely used singular value thresholding (SVT) operators associated with rank relaxation functions often face higher computational complexity, particularly for large-scale data matrices. To improve the efficacy of low-rank subspace clustering and overcome the issue of high computational complexity, this work proposes an efficient and effective method that avoids the need for singular value decomposition (SVD) computations in the iteration scheme. This can be achieved through the use of a computationally efficient and compact formulation, as well as automatic removal of the optimal mean, which reduces time consumption and enhances evaluation performance. A unified clustering framework based on Schatten-$p$norm regularized by$\ell _{2,q}$-norm can be formulated using this processing way, where inner element suppression can be achieved by choosing appropriate$p$,$q \in (0,1)$. Additionally, calculating the optimal mean enhances the robustness of the proposed method in the presence of outliers. Unlike the general iteration scheme of the alternating direction method of multiplier (ADMM) algorithms that introduce auxiliary splitting variables, the proposed alternating re-weighted least square (ARwLS) algorithm uses matrix inverse and multiplication computations to obtain analytic solutions, resulting in faster processing speeds for each sub-problem. To further investigate, we provide the computational complexity of each iteration and the theoretical analysis of the convergence property, where the derived solution is a stationary point. Experimental results on synthetic data and several benchmark datasets demonstrate the promising efficiency and efficacy of the proposed clustering method compared to classical and competing algorithms.

The non-local-based model for hyperspectral image (HSI) denoising first uses non-local self-similarity (NSS) prior to group similar full-band patches into three-dimensional non-local full-band groups (tensors) using a block matching (BM) operation, and then a low-rank (LR) penalty is typically applied to each non-local full-band group to reduce noise. While non-local-based methods have shown promising performance in HSI denoising, most existing methods have only considered the LR property of the non-local full-band group while ignoring the strong correlation between sparse coefficients. Moreover, such methods often result in unsatisfactory visual artifacts due to the noise sensitivity of BM operations, while requiring expensive computations. To address these limitations, this paper proposes a novel non-local structured sparsity regularization (NLSSR) approach for HSI denoising. First, to mitigate the noise sensitivity of the BM operation, we propose a graph-based domain distance scheme to index similar full-band patches to form the non-local full-band group. Second, we design an adaptive unidirectional low-rank (LR) dictionary with low complexity that takes into account the differences in intrinsic structure correlation among different modes of the non-local full-band tensor. Third, we utilize a global spectral LR prior to reduce spectral redundancy. Fourth, we develop a generalized soft-thresholding (GST) algorithm based on the alternating minimization framework to solve the NLSSR-based HSI denoising problem. We perform extensive experiments on both simulated and real data to show that the proposed NLSSR algorithm outperforms many popular or state-of-the-art HSI denoising methods in both quantitative and visual evaluations.

As a spotlighted nonlocal image representation model, group sparse representation (GSR) has demonstrated a great potential in diverse image restoration tasks. Most of the existing GSR-based image restoration approaches exploit the nonlocal self-similarity (NSS) prior by clustering similar patches into groups and imposing sparsity to each group coefficient, which can effectively preserve image texture information. However, these methods have imposed only plain sparsity over each individual patch of the group, while neglecting other beneficial image properties, e.g., low-rankness (LR), leads to degraded image restoration results. In this article, we propose a novel low-rankness guided group sparse representation (LGSR) model for highly effective image restoration applications. The proposed LGSR jointly utilizes the sparsity and LR priors of each group of similar patches under a unified framework. The two priors serve as the complementary priors in LGSR for effectively preserving the texture and structure information of natural images. Moreover, we apply an alternating minimization algorithm with an adaptively adjusted parameter scheme to solve the proposed LGSR-based image restoration problem. Extensive experiments are conducted to demonstrate that the proposed LGSR achieves superior results compared with many popular or state-of-the-art algorithms in various image restoration tasks, including denoising, inpainting, and compressive sensing (CS).

Poisson noise is a common electronic noise, which has widely occurred in various photo-limited imaging systems. However, due to signal-dependent and multiplicative characteristics for Poisson noise, Poisson denoising is still an open problem. In this paper, we propose a novel approach using simultaneous nonlocal low-rank and deep priors (SNLDP) for Poisson denoising. The proposed SNLD-P simultaneously employs nonlocal self-similarity and deep image priors under the hybrid plug and play framework, which comprises multiple pairs of complementary priors, namely, nonlocal and local, shallow and deep, and internal and external. To make the optimization tractable, an effective alternating direction method of multiplier (ADMM) algorithm under the alternative minimization framework is provided to solve the proposed SNLDP-based Poisson denoising problem. Experimental results demonstrate the superiority of the proposed SNLDP over many popular or state-of-the-art Poisson denoising algorithms in terms of quantitative and visual perception.

This article proposes a novel nonconvex structural sparsity residual constraint (NSSRC) model for image restoration, which integrates structural sparse representation (SSR) with nonconvex sparsity residual constraint (NC-SRC). Although SSR itself is powerful for image restoration by combining the local sparsity and nonlocal self-similarity in natural images, in this work, we explicitly incorporate the novel NC-SRC prior into SSR. Our proposed approach provides more effective sparse modeling for natural images by applying a more flexible sparse representation scheme, leading to high-quality restored images. Moreover, an alternating minimizing framework is developed to solve the proposed NSSRC-based image restoration problems. Extensive experimental results on image denoising and image deblocking validate that the proposed NSSRC achieves better results than many popular or state-of-the-art methods over several publicly available datasets.

Constructing effective priors is critical to solving ill-posed inverse problems in image processing and computational imaging. Recent works focused on exploiting non-local similarity by grouping similar patches for image modeling, and demonstrated state-of-the-art results in many image restoration applications. However, compared to classic methods based on filtering or sparsity, non-local algorithms are more time-consuming, mainly due to the highly inefficient block matching step, i.e., distance between every pair of overlapping patches needs to be computed. In this work, we propose a novel Self-Convolution operator to exploit image non-local properties in a unified framework. We prove that the proposed Self-Convolution based formulation can generalize the commonly-used non-local modeling methods, as well as produce results equivalent to standard methods, but with much cheaper computation. Furthermore, by applying Self-Convolution, we propose an effective multi-modality image restoration scheme, which is much more efficient than conventional block matching for non-local modeling. Experimental results demonstrate that (1) Self-Convolution with fast Fourier transform implementation can significantly speed up most of the popular non-local image restoration algorithms, with two-fold to nine-fold faster block matching, and (2) the proposed online multi-modality image restoration scheme achieves superior denoising results than competing methods in both efficiency and effectiveness on RGB-NIR images. The code for this work is publicly available at https://github.com/GuoLanqing/Self-Convolution.

Spectral computed tomography (CT) reconstructs images from different spectral data through photon counting detectors (PCDs). However, due to the limited number of photons and the counting rate in the corresponding spectral segment, the reconstructed spectral images are usually affected by severe noise. In this paper, we propose a fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction (FONT-SIR). To maintain the original spatial relationships among similar patches and improve the imaging quality, similar patches without vectorization are grouped in both spectral and spatial domains simultaneously to form the fourth-order processing tensor unit. The similarity of different patches is measured with the cosine similarity of latent features extracted using principal component analysis (PCA). By imposing the constraints of the weighted nuclear and total variation (TV) norms, each fourth-order tensor unit is decomposed into a low-rank component and a sparse component, which can efficiently remove noise and artifacts while preserving the structural details. Moreover, the alternating direction method of multipliers (ADMM) is employed to solve the decomposition model. Extensive experimental results on both simulated and real data sets demonstrate that the proposed FONT-SIR achieves superior qualitative and quantitative performance compared with several state-of-the-art methods.

Recent works on structural sparse representation (SSR), which exploit image nonlocal self-similarity (NSS) prior by grouping similar patches for processing, have demonstrated promising performance in various image restoration applications. However, conventional SSR-based image restoration methods directly fit the dictionaries or transforms to the internal (corrupted) image data. The trained internal models inevitably suffer from overfitting to data corruption, thus generating the degraded restoration results. In this article, we propose a novel hybrid structural sparsification error (HSSE) model for image restoration, which jointly exploits image NSS prior using both the internal and external image data that provide complementary information. Furthermore, we propose a general image restoration scheme based on the HSSE model, and an alternating minimization algorithm for a range of image restoration applications, including image inpainting, image compressive sensing and image deblocking. Extensive experiments are conducted to demonstrate that the proposed HSSE-based scheme outperforms many popular or state-of-the-art image restoration methods in terms of both objective metrics and visual perception.

Constructing effective image priors is critical to solving ill-posed inverse problems, such as image restoration. Recent works proposed to exploit image non-local similarity for inverse problems by grouping similar patches, and demonstrated state-of-the-art results in many applications. However, comparing to classic local methods based on filtering or sparsity, most of the non-local algorithms are time-consuming, mainly due to the highly inefficient and redundant block matching step, where the distance between each pair of overlapping patches needs to be computed. In this work, we propose a novel Self-Convolution operator to exploit image non-local similarity in a self-supervised way. The proposed Self-Convolution can generalize the commonly-used block matching step, and produce the equivalent results with much cheaper computation. Based on Self-Convolution, we propose an effective multi-modality image restoration scheme, which is much more efficient than conventional block matching for non-local modeling. Experimental results also demonstrate that Self-Convolution can significantly speed up most of the popular non-local image restoration algorithms, with two-fold to nine-fold faster block matching. The codes will be released on GitHub.

State-of-the-art image denoisers exploit various types of deep neural networks via deterministic training. Alternatively, very recent works utilize deep reinforcement learning for restoring images with diverse or unknown corruptions. Though deep reinforcement learning can generate effective policy networks for operator selection or architecture search in image restoration, how it is connected to the classic deterministic training in solving inverse problems remains unclear. In this work, we propose a novel image denoising scheme via Residual Recovery using Reinforcement Learning, dubbed R3L. We show that R3L is equivalent to a deep recurrent neural network that is trained using a stochastic reward, in contrast to many popular denoisers using supervised learning with deterministic losses. To benchmark the effectiveness of reinforcement learning in R3L, we train a recurrent neural network with the same architecture for residual recovery using the deterministic loss, thus to analyze how the two different training strategies affect the denoising performance. With such a unified benchmarking system, we demonstrate that the proposed R3L has better generalizability and robustness in image denoising when the estimated noise level varies, comparing to its counterparts using deterministic training, as well as various state-of the-art image denoising algorithms.

Nonlocal sparse representation models such as group sparse representation (GSR), low-rankness and joint sparsity (JS) have shown great potentials in image denoising studies, by effectively exploiting image nonlocal self-similarity (NSS) property. Popular dictionary-based JS algorithms apply convex JS penalties in their objective functions, which avoid NP-hard sparse coding step, but lead to only approximately sparse representation. Such approximated JS models fail to impose low-rankness of the underlying image data, resulting in degraded quality in image restoration. To simultaneously exploit the low-rank and JS priors, we propose a novel low-rank regularized joint sparsity model, dubbed LRJS, to enhance the dependency (i. e., low-rankness) of similar patches, thus better suppress independent noise. Moreover, to make the optimization tractable and robust, an alternating minimization algorithm with an adaptive parameter adjustment strategy is developed to solve the proposed LRJS-based image denoising problem. Experimental results demonstrate that the proposed LRJS outperforms many popular or state-of-the-art denoising algorithms in terms of both objective and visual perception met-

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, e.g., JS enforces the sparse codes to share the same support, or too general, e.g., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely, low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. An alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem for different image restoration tasks, including image denoising, image deblocking, image inpainting, and image compressive sensing. Extensive experimental results demonstrate that the proposed LR-GSC algorithm outperforms many popular or state-of-the-art methods in terms of objective and perceptual metrics.

Recent works that utilized deep models have achieved superior results in various image restoration (IR) applications. Such approach is typically supervised, which requires a corpus of training images with distributions similar to the images to be recovered. On the other hand, the shallow methods, which are usually unsupervised remain promising performance in many inverse problems, e.g., image deblurring and image compressive sensing (CS), as they can effectively leverage nonlocal self-similarity priors of natural images. However, most of such methods are patch-based leading to the restored images with various artifacts due to naive patch aggregation in addition to the slow speed. Using either approach alone usually limits performance and generalizability in IR tasks. In this paper, we propose a joint low-rank and deep (LRD) image model, which contains a pair of triply complementary priors, namely, internal and external, shallow and deep, and non-local and local priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on the LRD model for IR. Following this, a simple yet effective algorithm is developed to solve the proposed H-PnP based IR problems. Extensive experimental results on several representative IR tasks, including image deblurring, image CS and image deblocking, demonstrate that the proposed H-PnP algorithm achieves favorable performance compared to many popular or state-of-the-art IR methods in terms of both objective and visual perception.

Inspired by the image nonlocal self-similarity (NSS) prior, structural sparse representation (SSR) models exploit each group as the basic unit for sparse representation, which have achieved promising results in various image restoration applications. However, conventional SSR models only exploited the group within the input degraded (internal) image for image restoration, which can be limited by over-fitting to data corruption. In this paper, we propose a novel hybrid structural sparse error (HSSE) model for image deblocking. The proposed HSSE model exploits image NSS prior over both the internal image and external image corpus, which can be complementary in both feature space and image plane. Moreover, we develop an alternating minimization with an adaptive parameter setting strategy to solve the proposed HSSE model. Experimental results demonstrate that the proposed HSSE-based image deblocking algorithm outperforms many state-of-the-art image deblocking methods in terms of objective and visual perception.

Recent works that utilized deep models have achieved superior results in various image restoration applications. Such approach is typically supervised which requires a corpus of training images with distribution similar to the images to be recovered. On the other hand, the shallow methods which are usually unsupervised remain promising performance in many inverse problems, e.g., image compressive sensing (CS), as they can effectively leverage non-local self-similarity priors of natural images. However, most of such methods are patch-based leading to the restored images with various ringing artifacts due to naive patch aggregation. Using either approach alone usually limits performance and generalizability in image restoration tasks. In this paper, we propose a joint low-rank and deep (LRD) image model, which contains a pair of triply complementary priors, namely external and internal, deep and shallow, and local and nonlocal priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on the LRD model for image CS. To make the optimization tractable, a simple yet effective algorithm is proposed to solve the proposed H-PnP based image CS problem. Extensive experimental results demonstrate that the proposed H-PnP algorithm significantly outperforms the state-of-the-art techniques for image CS recovery such as SCSNet and WNNM.

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, i.e., JS enforces the sparse codes to share the same support, or too general, i.e., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. To make the proposed scheme tractable and robust, an alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem. Experimental results on both image deblocking and denoising demonstrate that the proposed LR-GSC image restoration algorithms outperform many popular or state-of-the-art methods, in terms of 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 state-of-the-art image inpainting and image CS recovery methods in terms of both objective and perceptual quality metrics.

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.

Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work attempts to fill the gap from the perspective of rank minimization. We firstly design an adaptive dictionary to bridge the gap between group-based sparse coding (GSC) and rank minimization. Then, we show that under the designed dictionary, GSC and the rank minimization problems are equivalent, and therefore the sparse coefficients of each patch group can be measured by estimating the singular values of each patch group. We thus earn a benchmark to measure the sparsity of each patch group because the singular values of the original image patch groups can be easily computed by the singular value decomposition (SVD). This benchmark can be used to evaluate performance of any kind of norm minimization methods in sparse coding through analyzing their corresponding rank minimization counterparts. Towards this end, we exploit four well-known rank minimization methods to study the sparsity of each patch group and the weighted Schatten p-norm minimization (WSNM) is found to be the closest one to the real singular values of each patch group. Inspired by the aforementioned equivalence regime of rank minimization and GSC, WSNM can be translated into a non-convex weighted ℓp-norm minimization problem in GSC. By using the earned benchmark in sparse coding, the weighted ℓp-norm minimization is expected to obtain better performance than the three other norm minimization methods, i.e., ℓ1-norm, ℓp-norm and weighted ℓ1-norm. To verify the feasibility of the proposed benchmark, we compare the weighted ℓp-norm minimization against the three aforementioned norm minimization methods in sparse coding. Experimental results on image restoration applications, namely image inpainting and image compressive sensing recovery, demonstrate that the proposed scheme is feasible and outperforms many state-of-the-art methods.

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.

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 paper, 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.

The nuclear norm minimization (NNM) is commonly used to approximate the matrix rank by shrinking all singular values equally. However, the singular values have clear physical meanings in many practical problems, and NNM may not be able to faithfully approximate the matrix rank. To alleviate the above-mentioned limitation of NNM, recent studies have suggested that the weighted nuclear norm minimization (WNNM) can achieve a better rank estimation than NNM, which heuristically set the weight being inverse to the singular values. However, it still lacks a rigorous explanation why WNNM is more effective than NMM in various applications. In this paper, we analyze NNM and WNNM from the perspective of group sparse representation (GSR). Concretely, an adaptive dictionary learning method is devised to connect the rank minimization and GSR models. Based on the proposed dictionary, we prove that NNM and WNNM are equivalent to ℓ1-norm minimization and the weighted ℓ1-norm minimization in GSR, respectively. Inspired by enhancing sparsity of the weighted ℓ1-norm minimization in comparison with ℓ1-norm minimization in sparse representation, we thus explain that WNNM is more effective than NMM. By integrating the image nonlocal self-similarity (NSS) prior with the WNNM model, we then apply it to solve the image denoising problem. Experimental results demonstrate that WNNM is more effective than NNM and outperforms several state-of-the-art methods in both objective and perceptual quality.

Nonlocal image representation has achieved great success in various image processing tasks such as image denoising, image deblurring and image deblocking. Particularly, by exploiting the image nonlo-cal self-similarity (NSS) prior, many nonlocal similar patches can be searched across the whole image for a given patch, which has significantly boosted the performance of image restoration. To the best of our knowledge, most existing methods only consider the NSS prior of the input degraded image, while few methods exploit the NSS prior from external clean image corpus. However, how to utilize the NSS priors of input degraded image and external clean image corpus simultaneously is still an open problem. In this paper, we propose a novel approach for image denoising, which exploits simultaneous nonlocal self-similarity (SNSS) by integrating the NSS priors of both the input degraded image and external clean image corpus. Firstly, we search and group nonlocal similar patches from a clean image corpus, and a group-based Gaussian Mixture Model (GMM) learning algorithm is developed to learn an external NSS prior. Then, an optimal group is selected from the best suitable Gaussian component for a group of the noisy image. By integrating the group of the noisy image and the corresponding group of the Gaussian component with a low-rank constraint, an iterative algorithm is developed to solve the proposed SNSS model. Experimental results demonstrate that the proposed SNSS-based denoising method produces superior results compared with many state-of-the-art denoising methods in both objective and perceptual quality.

Sparse representation has achieved great successes in various machine learning and image processing 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 produce over-smooth phenomena. 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 a powerful mechanism to integrate the local sparsity and nonlocal self-similarity of images. We then apply the proposed JPG-SR model to a low-level vision problem, namely, image inpainting. To make the proposed scheme tractable and robust, an iterative algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed JPG-SR model. Experimental results demonstrate that the proposed model is efficient and outperforms several state-of-the-art methods in both objective and perceptual quality.

Inspired by group-based sparse coding, recently proposed group sparsity residual (GSR) scheme has demonstrated superior performance in image processing. However, one challenge in GSR is to estimate the residual by using a proper reference of the group-based sparse coding (GSC), which is desired to be as close to the truth as possible. Previous researches utilized the estimations from other algorithms (i.e., GMM or BM3D), which are either not accurate or too slow. In this paper, we propose to use the Non-Local Samples (NL-S) as reference in the GSR regime for image denoising, thus termed GSR-NLS. More specifically, we first obtain a good estimation of the group sparse coefficients by the image nonlocal self-similarity, and then solve the GSR model by an effective iterative shrinkage algorithm. Experimental results demonstrate that the proposed GSR-NLS not only outperforms many state-of-the-art methods, but also delivers the competitive advantage of speed.

Group sparsity has shown great potential in various low-level vision tasks (e.g, image denoising, deblurring and inpainting). In this paper, we propose a new prior model for image denoising via group sparsity residual constraint (GSRC). To enhance the performance of group sparse-based image denoising, the concept of group sparsity residual is proposed, and thus, the problem of image denoising is translated into one that reduces the group sparsity residual. To reduce the residual, we first obtain some good estimation of the group sparse coefficients of the original image by the first-pass estimation of noisy image, and then centralize the group sparse coefficients of noisy image to the estimation. Experimental results have demonstrated that the proposed method not only outperforms many state-of-the-art denoising methods such as BM3D and WNNM, but results in a faster speed.

Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, due to a majority of reconstruction methods only exploit the nonlocal self-similarity (NSS) prior of the degraded observation image, it is very challenging to reconstruct the latent clean image directly from the noisy observation. In this paper we propose a novel model for image denoising via group sparsity residual and external NSS prior. To boost the performance of image denoising, the concept of group sparsity residual is proposed, and thus the problem of image denoising is transformed into one that reduces the group sparsity residual. Due to the fact that the groups contain a large amount of NSS information of natural images, we obtain a good estimation of the group sparse coefficients of the original image by the external NSS prior based on Gaussian Mixture model (GMM) learning and the group sparse coefficients of noisy image are used to approximate the estimation. Experimental results demonstrate that the proposed approach not only outperforms many state-of-the-art methods, but also delivers the best qualitative denoising results with finer details and less ringing artifacts.

Sparse coding has achieved a great success in various image processing studies. However, there is not any benchmark to measure the sparsity of image patch/group because sparse discriminant conditions cannot keep unchanged. This paper analyzes the sparsity of group based on the strategy of the rank minimization. Firstly, an adaptive dictionary for each group is designed. Then, we prove that group-based sparse coding is equivalent to the rank minimization problem, and thus the sparse coefficients of each group are measured by estimating the singular values of each group. Based on that measurement, the weighted Schatten p-norm minimization (WSNM) has been found to be the closest solution to the real singular values of each group. Thus, WSNM can be equivalently transformed into a non-convex ℓp-norm minimization problem in group-based sparse coding. Experimental results on two applications: image in painting and image compressive sensing (CS) recovery show that the proposed scheme outperforms many state-of-the-art methods.

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, learned simultaneous sparse coding. In the past, convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise. However, using convex regularization cannot still obtain the correct sparsity solution under some practical problems including image inverse problems. In this letter, we propose a nonconvex weighted ℓpminimization based group sparse representation framework for image denoising. To make the proposed scheme tractable and robust, the generalized soft-thresholding algorithm is adopted to solve the nonconvex ℓpminimization problem. In addition, to improve the accuracy of the nonlocal similar patch selection, an adaptive patch search scheme is proposed. Experimental results demonstrate that the proposed approach not only outperforms many state-of-the-art denoising methods such as BM3D and weighted nuclear norm minimization, but also results in a competitive speed.