Image colorization based on ADMM with fast singular value thresholding by Chebyshev polynomial approximation

Abstract

We propose an image colorization method using fast soft-thresholding of singular values (singular value thresholding). An image colorization method with nuclear norm minimization (NNM) has been proposed and brings good results. NNM usually requires iterative application of singular value decomposition (SVD) for singular value thresholding. However, the computational cost of SVD in the colorization method becomes too expensive to handle highresolution images. In this paper, we reduce its computational cost by using Chebyshev polynomial approximation (CPA). Singular value thresholding is expressed by a multiplication of certain matrices derived from the characteristic of CPA. As a result, our CPA-based technique makes the image colorization method much more efficient. In addition, we replace the optimization method used in the image colorization method by alternating direction method of multipliers, which further accelerates the computation. Experimental results verify the effectiveness of our method with respect to the computation time and the approximation precision.