Improved quaternion robust principal component analysis for color image recovery

Numerous studies have demonstrated the potential of robust principal component analysis (RPCA) in image recovery. However, conventional RPCA methods for color image recovery apply RPCA independently to each color channel, which ignores the correlation information of the red, green and blue channels. To improve the performance of RPCA-based methods and draw inspiration from the success of quaternion representation in color image processing, we propose an improved quaternion RPCA (IQRPCA) method for color image recovery. The IQRPCA method treats all color channels holistically and considers the correlation information of different color channels naturally. In addition, we have developed a quaternion nuclear norm known as improved quaternion Cauchy nuclear norm, which produces an even more effective and robust approach to color image recovery task. Compared to the RPCA method in the quaternion setting, the IQRPCA method treats the singular values differently, which shows better recovery performance than competing methods. Furthermore, we provide a convergence analysis of the proposed method. Our experiments confirm the effectiveness of IQRPCA in the application of color image recovery.