Total Variation Based Pure Quaternion Dictionary Learning Method for Color Image Denoising

As an important pre-processing step for many related computer vision tasks, color image denoising has attracted considerable attention in image processing. However, traditional methods often regard the red, green, and blue channels of color images independently without considering the correlations among the three channels. In order to overcome this deficiency, this paper proposes a novel dictionary method for color image denoising based on pure quaternion representation, which efficiently deals with both single-channel and cross-channel information. The pure quaternion constraint is firstly used to force the sparse representations of color images to contain only red, green, and blue color information. Moreover, a total variation regularization is proposed in the quaternion domain and embedded into the pure quaternion-based representation model, which is effective to recover the sharp edges of color images. To solve the proposed model, a new numerical scheme is also developed based on the alternating minimization method (AMM). Experimental results demonstrate that the proposed model has better denoising results than the state-of-the-art methods, including a deep learning approach DnCNN, in terms of PSNR, SSIM, and visual quality.