Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction
This method improves color image quality for low-level vision applications, though it appears incremental as it builds on quaternion-based approaches with a new regularization technique.
The paper tackles color image reconstruction by addressing inter-channel correlation issues, introducing Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF) to reduce color distortion and artifacts, achieving state-of-the-art results in tasks like denoising and deblurring.
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.