用四元数建模彩色图像通道关系，修复效果更优
Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction
- 用四元数统一表示RGB三通道，捕捉颜色相关性
- 核范数减弗罗贝尼乌斯范数正则化，逼近低秩结构
- 在去噪、去模糊等任务中达到顶尖效果，适合图像修复
彩色图像恢复方法通常将图像表示为欧几里得空间中的向量或三个灰度通道的组合，但常忽略通道间的关联性，导致重建图像出现色彩失真和伪影。为此，本文提出四元数核范数减弗罗贝尼乌斯范数最小化（QNMF）方法，利用四元数代数全面捕获RGB通道间的关系。通过引入核范数减弗罗贝尼乌斯范数的正则化技术，QNMF近似四元数编码彩色图像的潜在低秩结构。理论证明确保了方法的数学严谨性。实验表明，该正则化器在多种彩色低层视觉任务中表现卓越，包括去噪、去模糊、补全和随机脉冲噪声去除，均取得当前最优性能。
原文摘要 · Abstract (English)
Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.
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