A fast optimization transfer algorithm for image inpainting in wavelet domains

  • Authors:

  • Raymond H. Chan;You-Wei Wen;Andy M. Yip

  • Affiliations:

  • Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong;Approximation and Information Processing, Temasek Laboratories, Centre for Wavelets, National University of Singapore, Singapore and Faculty of Science, South China Agricultural University, Wushan ...;Department of Mathematics, National University of Singapore, Singapore

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 2009

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Abstract

A wavelet inpainting problem refers to the problem of filling in missing wavelet coefficients in an image. A variational approach was used by Chan et al. The resulting functional was minimized by the gradient descent method. In this paper, we use an optimization transfer technique which involves replacing their univariate functional by a bivariate functional by adding an auxiliary variable. Our bivariate functional can be minimized easily by alternating minimization: for the auxiliary variable, the minimum has a closed form solution, and for the original variable, the minimization problem can be formulated as a classical total variation (TV) denoising problem and, hence, can be solved efficiently using a dual formulation. We show that our bivariate functional is equivalent to the original univariate functional. We also show that our alternating minimization is convergent. Numerical results show that the proposed algorithm is very efficient and outperforms that of Chan et al.