Quaternion optimized model with sparseness for color image recovery

This paper presents a novel approach for sparse regularization of low-rank quaternion matrix optimization problems. Quaternion matrices, which extend the concept of complex numbers to four dimensions, have shown promising applications in various fields. In this work, we exploit the inherent sparsity present in different signal types, such as audio formats and images, when represented in their respective bases. By introducing a sparse regularization term in the optimization objective. We propose a regularization technique that promotes sparsity in the Quaternion Discrete Cosine Transform (QDCT) domain for efficient and accurate solutions. By combining low-rank restriction with sparsity, the optimized model is updated using a two-step Alternating Direction Method of Multipliers (ADMM) algorithm. Experimental results on color images demonstrate the effectiveness of the proposed method, which outperforms existing relative methods. This superior performance underscores its potential for applications in computer vision and related fields.