A Trilateral Weighted Sparse Coding Scheme for Real-World Image Denoising (1807.04364v1)

Abstract: Most of existing image denoising methods assume the corrupted noise to be additive white Gaussian noise (AWGN). However, the realistic noise in real-world noisy images is much more complex than AWGN, and is hard to be modelled by simple analytical distributions. As a result, many state-of-the-art denoising methods in literature become much less effective when applied to real-world noisy images captured by CCD or CMOS cameras. In this paper, we develop a trilateral weighted sparse coding (TWSC) scheme for robust real-world image denoising. Specifically, we introduce three weight matrices into the data and regularisation terms of the sparse coding framework to characterise the statistics of realistic noise and image priors. TWSC can be reformulated as a linear equality-constrained problem and can be solved by the alternating direction method of multipliers. The existence and uniqueness of the solution and convergence of the proposed algorithm are analysed. Extensive experiments demonstrate that the proposed TWSC scheme outperforms state-of-the-art denoising methods on removing realistic noise.

• The paper proposes the Trilateral Weighted Sparse Coding (TWSC) scheme, which enhances sparse coding to handle complex, non-Gaussian noise in real-world images by incorporating three weight matrices.
• TWSC integrates three weight matrices: two in the data-fidelity term to model channel-wise and patch-wise noise, and one in the regularization term based on image sparsity priors.
• Experimental results show TWSC consistently outperforms state-of-the-art methods on real-world noisy datasets, demonstrating a significant advance for practical image denoising applications.

Trilateral Weighted Sparse Coding for Real-World Image Denoising

This paper presents a novel trilateral weighted sparse coding (TWSC) scheme tailored for the denoising of real-world images, which are often corrupted by noise more complex than the commonly addressed additive white Gaussian noise (AWGN). The authors highlight the inadequacies of traditional denoising methods, which assume AWGN, when tackling real-world scenarios where noise presents significant complexity due to factors such as signal dependency and varying camera settings (e.g., ISO, shutter speed).

Problem Statement

The challenge addressed in this paper is the removal of noise from images captured by CCD or CMOS cameras, where the noise deviates from the simple AWGN model. This noise is signal-dependent, non-Gaussian, and varies across different local patches and channels, posing a substantial challenge to existing denoising techniques that have demonstrated efficacy under the AWGN assumption.

Proposed Methodology

The authors propose enhancing the sparse coding (SC) framework by integrating three distinct weight matrices into both the data-fidelity and regularization terms of the SC model. This forms the basis of the Trilateral Weighted Sparse Coding (TWSC) scheme:

1. Data-Fidelity Term Weighting: Two weight matrices are introduced to characterize the channel-wise and patch-wise noise statistics, thereby tailoring the SC model to better accommodate the complex noise observed in real-world images.
2. Regularization Term Weighting: A third weight matrix is introduced to reflect prior knowledge about the sparsity of natural images, improving the regularization of the sparse coding coefficients.

The problem is formulated as a linear equality-constrained optimization problem and is solved using the Alternating Direction Method of Multipliers (ADMM). The authors also provide a thorough theoretical analysis of the existence and uniqueness of solutions and propose computational improvements for solving the Sylvester equation central to the ADMM updates.

Experimental Results

The effectiveness of the TWSC approach is validated through extensive experiments on synthetic and real-world noisy datasets. The evaluation includes a rigorous comparison with state-of-the-art denoising methods such as CBM3D, TNRD, DnCNN, as well as commercial software like Neat Image (NI). The TWSC scheme consistently outperforms these baseline methods, particularly in real-world noise scenarios. Notable improvements are recorded in both PSNR and SSIM metrics across multiple datasets, such as the Darmstadt Noise Dataset (DND) and others provided by [24] and [49].

Implications

The TWSC scheme represents a significant advance in the domain of image denoising, demonstrating superior performance in handling realistic noise in natural images. By integrating channel-wise and patch-wise noise characterizations with the sparse coding framework, the TWSC method offers a robust solution for practical applications in photography and computer vision.

Future Directions

This work provides a groundwork that could spark further investigations into adaptive weight matrix designs and their applications in different domains where noise characteristics deviate from simplistic models. Future research might explore deeper integrations of sparse coding with generative models or investigate more efficient real-time implementations for practical applications.

In conclusion, this trilateral approach broadens the toolkit available for image processing in complex real-world environments, with significant potential for future exploitation and development in AI-driven vision systems.