Blind Deconvolution for Color Images Using Normalized Quaternion Kernels
Yuming Yang, Michael K. Ng, Zhigang Jia, Wei Wang
TL;DR
Addresses the color image blind deconvolution problem under the forward model $f = k \star u + n$, proposing a quaternion convolution kernel with four components to capture cross-channel channel interdependencies and a normalization scheme to preserve intensity. The method introduces a quaternion data-fitting term $\\|\\mathbf{Q} \\circledast \\mathbf{u} - \\mathbf{f}\\|_2^2$ within the $L_0$ + X framework and enables efficient optimization via FFT-based solvers. Extensions with priors like dark-channel or surface-aware prior are described. Experiments on synthetic and real blurred color images show improved artifact suppression and color fidelity, suggesting a powerful tool for color image deconvolution.
Abstract
In this work, we address the challenging problem of blind deconvolution for color images. Existing methods often convert color images to grayscale or process each color channel separately, which overlooking the relationships between color channels. To handle this issue, we formulate a novel quaternion fidelity term designed specifically for color image blind deconvolution. This fidelity term leverages the properties of quaternion convolution kernel, which consists of four kernels: one that functions similarly to a non-negative convolution kernel to capture the overall blur, and three additional convolution kernels without constraints corresponding to red, green and blue channels respectively model their unknown interdependencies. In order to preserve image intensity, we propose to use the normalized quaternion kernel in the blind deconvolution process. Extensive experiments on real datasets of blurred color images show that the proposed method effectively removes artifacts and significantly improves deblurring effect, demonstrating its potential as a powerful tool for color image deconvolution.