Source-linked AI summary
Depth image denoising using nuclear norm and learning graph model
Chenggang Yan, Zhisheng Li, Yongbing Zhang, Yutao Liu, Xiangyang Ji, Yongdong Zhang
TL;DR
Noisy depth-camera images motivate denoising methods that preserve their internal structure. The paper proposes GNNLG, combining grouped low-rank modeling with a learned graph prior and ADMM optimization, and reports best PSNR against many state-of-the-art techniques, along with high convergence and stable, self-adaptive behavior.
Problem
Depth images acquired by depth cameras are corrupted by noise, while conventional methods do not account for internal image relations and can under-fit or over-fit.
Method
GNNLG groups similar patches, exploits their low-rank structure, learns a graph Laplacian for smoothing, and uses ADMM with a fast threshold algorithm.
Results
GNNLG achieves best PSNR compared to many current state-of-the-art denoising techniques, with high convergence, stability, and self-adaptiveness reported.
Takeaways & Limitations
The reported results support GNNLG as a depth-image denoising framework combining low-rank, self-similarity, and graph-based smoothing priors.
Takeaways & Limitations
Sparse dictionary approaches are non-convex and often computationally complex, motivating the paper’s alternative optimization strategy.
Abstract
from arXiv · showhide
The depth images denoising are increasingly becoming the hot research topic nowadays because they reflect the three-dimensional (3D) scene and can be applied in various fields of computer vision. But the depth images obtained from depth camera usually contain stains such as noise, which greatly impairs the performance of depth related applications. In this paper, considering that group-based image restoration methods are more effective in gathering the similarity among patches, a group based nuclear norm and learning graph (GNNLG) model was proposed. For each patch, we find and group the most similar patches within a searching window. The intrinsic low-rank property of the grouped patches is exploited in our model. In addition, we studied the manifold learning method and devised an effective optimized learning strategy to obtain the graph Laplacian matrix, which reflects the topological structure of image, to further impose the smoothing priors to the denoised depth image. To achieve fast speed and high convergence, the alternating direction method of multipliers (ADMM) is proposed to solve our GNNLG. The experimental results show that the proposed method is superior to other current state-of-the-art denoising methods in both subjective and objective criterion.
1 INTRODUCTION
Depth-camera images are noisy, motivating denoising methods that exploit internal image structure. The proposed GNNLG framework combines grouped low-rank modeling with a learned graph prior and is reported to outperform state-of-the-art methods.
- Depth images describe distances between 3D objects and the camera plane but are corrupted by noise from imperfect depth-sensing technology.
- Conventional denoising methods often neglect internal image relations, which can produce under-fitting or over-fitting results.
- Nonlocal self-similarity among similar patches and manifold graphs provide complementary priors for modeling image structure.
- GNNLG combines grouped patches, nuclear-norm low-rank modeling, and a learned graph Laplacian to exploit self-similarity and impose smoothing.
- ADMM solves the proposed model, while a fast threshold algorithm addresses the nuclear-norm subproblem instead of conventional soft thresholding.
- The experiments report that GNNLG outperforms other state-of-the-art denoising methods in subjective and objective criteria.
2 RELATED WORK
Image denoising research has progressed from conventional filtering toward methods that exploit sparsity, low rank, self-similarity, and graph structure. However, conventional spatial and transform-domain methods can ignore inherent image properties and produce blurry results.
- Conventional filtering: Conventional spatial and transform-domain filtering methods form the early foundation of image denoising research.Wavelet, Fourier, mean, and related filtering approaches are described as established methods.
- Limitations: These conventional methods ignore inherent image properties, which can result in blurry denoised images.
- Sparse representation: Sparse representation and dictionary-learning methods model image structure for restoration and denoising.The related work includes sparse decomposition, K-SVD, learned dictionaries, and clustering-based sparse representation.
- Low-rank methods: Low-rank priors and nuclear-norm minimization have been applied to depth-image denoising and matrix recovery.The nuclear norm approximately represents a matrix’s low-rank structure, while weighted nuclear norm minimization extends this approach.
- Self-similarity and grouping: Self-similarity methods use relationships among nonlocal patches, including NLM, BM3D, and group-based sparse representation.Group-based frameworks are reported to significantly improve denoising performance, while BM3D combines spatial and transform-domain filtering.
- Graph models: Graph-based models exploit image relationships for reconstruction and denoising, with NLGBT identified as a state-of-the-art depth-image denoising algorithm.The cited graph approaches include tree-distance models, non-local graph-based transforms, and graph learning based on intrinsic image relationships.
3 ALGORITHM
The algorithm combines group-based graph priors, learned Laplacian matrices, and nuclear-norm regularization to denoise grouped similar patches. ADMM decomposes the resulting optimization into tractable subproblems, including a fast thresholding update.
- Group-based graph prior: Graph Laplacians encode data relationships and impose smoothing priors during denoising.The graph term is linked to the Laplacian trace and is described as important for denoising.
- Group-based graph prior: Overlapping patches are grouped with similar patches through block matching, and the group is modeled using dual row and column graphs.Row graphs capture similarity at corresponding positions across similar patches, while column graphs capture similarity across locations within each patch.
- Learning graph: The learned Laplacian is obtained by optimizing the graph model and Laplacian jointly under validity, effectiveness, and trace constraints.The learned graph is self-adaptive and is reported to ensure high smoothness for each data matrix.
- Nuclear norm model: The combined objective uses nuclear norm, row-graph, and column-graph regularization to exploit grouped low rank and nonlocal self-similarity.The nuclear norm represents low-rank structure, while graph regularization reflects nonlocal self-similarity.
- ADMM optimization: ADMM transforms the objective into X-, Z-, and dual-variable subproblems, enabling separate updates for the nuclear and graph terms.The X-subproblem is solved through SVD and a fast threshold operator Γλ,v.
- X-subproblem: The fast threshold operator interpolates between soft and hard thresholding: v near 1 gives soft thresholding, whereas v near 0 approximates hard thresholding.The threshold parameter λ is equivalent to θn/p in the X-subproblem.
4 RESULTS
Experiments evaluate GNNLG on eight depth images corrupted with AWGN at σ values from 15 to 30, using PSNR and visual comparisons. The method consistently outperforms competing denoising approaches while preserving details and converging effectively.
- Experimental setup: Experiments use eight depth images corrupted by additive white Gaussian noise with σ ranging from 15 to 30, evaluated primarily by PSNR.The images include Art, Books, Dolls, Moebius, Reindeer, Laundry, Cones, and Teddy.
- Algorithm: The implementation combines block matching, graph construction, nuclear-norm regularization, and ADMM-based iterative optimization.The denoising algorithm groups patches, learns graph Laplacian matrices, solves subproblems iteratively, and averages overlapping patches.
- Graph analysis: The learned graph removes more noise, preserves more details, and maintains sharper edges than the conventional graph on depth image Laundry.Its Laplacian matrices show darker, more textured diagonal regions associated with sharper edge preservation.
- Convergence: PSNR improves with outer iterations; for σ = 20 and σ = 30, it increases after two or three iterations before stabilizing on Art and Cones.At σ = 10, the overall iteration is reported as especially effective, and the authors describe the procedure as achieving strong convergence.
5 CONCLUSION
The conclusion presents GNNLG as a depth-image denoising framework that combines group-based low-rank modeling with learned graph regularization. Experiments report strong PSNR, visual quality, convergence, and stability relative to state-of-the-art methods.
- Contribution: GNNLG exploits the intrinsic low-rank and self-similarity properties of depth images through a group-based nuclear norm and learning graph.The framework constructs a graph Laplacian matrix through graph-learning regularization.
- Method: The learned graph Laplacian is intended to describe intrinsic self-similarity more effectively than tree-distance-based graph construction.ADMM is used to solve the resulting non-convex combination formulation.
- Results: GNNLG achieves the best PSNR compared with many current state-of-the-art denoising techniques.The conclusion reports this as the principal objective-quality outcome of the experiments.
- Algorithmic behavior: The algorithm exhibits high convergence and is described as stable and self-adaptive.The conclusion links these properties to the designed algorithm.
- Future work: Future work proposes adding dictionary learning, using deep learning for faster subproblem solutions, and extending GNNLG to super-resolution and deblurring.These directions are presented as extensions rather than achieved results.