研究目的
To propose a novel quaternion-based weighted nuclear norm minimization (QWNNM) model and algorithm for color image denoising that preserves the correlation among color channels and improves denoising performance.
研究成果
The proposed QWNNM method effectively denoises color images by preserving color channel correlations through quaternion representation and adaptive weighting of singular values. It outperforms existing methods in both quantitative metrics (PSNR and SSIM) and visual quality, especially when combined with Gaussian lowpass filtering for high noise levels. Future work should focus on improving computational efficiency and extending the method to other image processing tasks.
研究不足
The quaternion SVD is computationally intensive, leading to lower efficiency. The method may not perform as well as WNNM for very high noise levels (σn ≥ 75) without preprocessing, and the optimization can be sensitive to initial points in high-dimensional spaces.
1：Experimental Design and Method Selection:
The study uses a low-rank sparse framework with quaternion algebra to handle color images as whole entities. It involves extending weighted nuclear norm minimization (WNNM) to quaternion space, utilizing non-local similarity priors for patch grouping, and applying quaternion singular value decomposition (QSVD) for matrix decomposition.
2：Sample Selection and Data Sources:
Ten color images from the Berkeley Segmentation database and widely used images in digital image processing are used as test samples. Additive white Gaussian noise with different variances is added to generate noisy observations.
3：List of Experimental Equipment and Materials:
The experiments are implemented in MATLAB using a quaternion toolbox (Q-lib) for quaternion operations. No specific hardware is mentioned.
4：Experimental Procedures and Operational Workflow:
The algorithm involves dividing the noisy image into overlapping patches, finding similar patches using l2-norm distance, forming quaternion matrices, performing QSVD, applying weighted nuclear norm minimization with adaptive weights, and aggregating patches to reconstruct the denoised image. For high noise levels, a Gaussian lowpass filter is applied as preprocessing.
5：Data Analysis Methods:
Performance is evaluated using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) to compare with competing methods like K-SVD, QKSVD, and WNNM.
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