Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion

As an extension of Compressed Sensing(CS), Matrix Completion(MC) is widely applied to different fields. Recently, the Riemannian optimization based MC algorithm attracts a lot of attention from researchers due to its high accuracy in reconstruction and computational efficiency. Considering that the Riemannian optimization based MC algorithm assumes a fixed rank of the original matrix, and selects a random initial point for iteration, a novel algorithm is proposed, namely automatic rank estimation based Riemannian optimization matrix completion algorithm. In the proposed algorithm, the estimate of rank is obtained minimizing the objective function that involving the rank regulation, in addition, the iterative starting point is optimized based on Riemannian manifold. The Riemannian manifold based conjugate gradient method is then used to complete the matrix, thereby improving the reconstruction precision. The experimental results demonstrate that the image completion performance is significantly improved using the proposed algorithm, compared with several classical image completion methods.