Low-Rank Quaternion Approximation for Color Image Processing


Grayscale Image Processing has seen tremendous success with methods based on low-rank matrix approximation (LRMA). By default, LRMA restores each colour channel using the monochromatic model, alternatively it processes three separate colour channels by concatenating them. However, the significant correlation between RGB channels may be underutilised in these two systems. The LRQA model (low-rank quaternion approximation) is our solution to this problem. First, the colour image is encoded as a pure quaternion matrix, so that the cross-channel correlation of colour channels may be well exploited; second, the low-rank constraint is applied to the built-in quaternion matrix in standard sparse representation and LRMA-based approaches. An LRQA model based on numerous nonconvex functions is proposed to better estimate the singular values of the underlying low-rank matrix. LRQA outperforms numerous state-of-the-art sparse representation and LRMA-based approaches in terms of both quantitative measures and visual quality in colour picture denoising and inpainting tasks.

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