Wavelet algorithms for high-resolution image reconstruction

Raymond H. Chan, Tony F. Chan, Lixin Shen, Zuowei Shen

Research output: Contribution to journalArticlepeer-review

187 Scopus citations

Abstract

High-resolution image reconstruction refers to the reconstruction of high-resolution images from multiple low-resolution, shifted, degraded samples of a true image. In this paper, we analyze this problem from the wavelet point of view. By expressing the true image as a function in ℒ(ℝ 2), we derive iterative algorithms which recover the function completely in the ℒ sense from the given low-resolution functions. These algorithms decompose the function obtained from the previous iteration into different frequency components in the wavelet transform domain and add them into the new iterate to improve the approximation. We apply wavelet (packet) thresholding methods to denoise the function obtained in the previous step before adding it into the new iterate. Our numerical results show that the reconstructed images from our wavelet algorithms are better than that from the Tikhonov least-squares approach. Extension to super-resolution image reconstruction, where some of the low-resolution images are missing, is also considered.

Original languageEnglish (US)
Pages (from-to)1408-1432
Number of pages25
JournalSIAM Journal on Scientific Computing
Volume24
Issue number4
DOIs
StatePublished - Jan 2003

Keywords

  • High-resolution image reconstruction
  • Tikhonov least square method
  • Wavelet

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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