Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm.

Area of Science:

• Computer Vision
• Image Processing
• Data Science

Background:

• Quaternion representation offers advantages for color image processing.
• Matrix completion is crucial for recovering missing image data.
• Existing methods have limitations in handling complex image data.

Purpose of the Study:

• To propose a novel low-rank quaternion matrix completion algorithm.
• To recover missing data in color images efficiently and effectively.
• To combine low-rank decomposition and nuclear norm minimization for quaternion matrices.

Main Methods:

• Developed a quaternion matrix completion model integrating low-rank decomposition and nuclear norm minimization.
• Replaced the quaternion matrix nuclear norm with the sum of Frobenius norms of factor matrices.
• Transformed the quaternion domain problem into the complex domain using matrix equivalency.
• Employed an alternating minimization method for model optimization.

Main Results:

• The proposed algorithm demonstrates superior performance in color image recovery.
• The algorithm shows significant efficiency compared to existing tensor-based and quaternion-based methods.
• Successful reconstruction of missing data in color images was achieved.

Conclusions:

• The novel low-rank quaternion matrix completion algorithm is effective for color image recovery.
• The proposed method offers an efficient and superior alternative to current techniques.
• Quaternion-based matrix completion shows promise for advanced image processing applications.