Low-rank quaternion approximation for color image Processing

Abstract

Low-rank matrix approximation (LRMA)-based methods have made a great success for grayscale image processing. When handling color images, LRMA either restores each color channel independently using the monochromatic model or processes the concatenation of three color channels using the concatenation model. However, these two schemes may not make full use of the high correlation among RGB channels. To address this issue, we propose a novel low-rank quaternion approximation (LRQA) model. It contains two major components: first, instead of modeling a color image pixel as a scalar in conventional sparse representation and LRMA-based methods, the color image is encoded as a pure quaternion matrix, such that the cross-channel correlation of color channels can be well exploited; second, LRQA imposes the low-rank constraint on the constructed quaternion matrix. To better estimate the singular values of the underlying low-rank quaternion matrix from its noisy observation, a general model for LRQA is proposed based on several nonconvex functions.

Existing System

Low-Rank Quaternion Approximation (LRQA)

Proposed System

This system proposes a novel model, namely, low-rank quaternion approximation (LRQA) for color image processing. Different from LRMA-based methods treating color image pixel as a scalar, LRQA encodes each color image pixel as a pure quaternion number, such that more correlation information among RGB channels can be well preserved. To achieve a better quaternion rank estimation, we propose a general model for LRQA based on three nonconvex functions and derive a general solver. LRQA is further extended to handle the color image denoising and inpainting tasks. The experimental results on both simulated and real color images demonstrate their superiority over several state-of-the-art methods.

Architecture

BLOCK DIAGRAM