Wavelet algorithms for high-resolution image reconstruction

Raymond H. CHAN*, Tony F. CHAN, Lixin SHEN, Zuowei SHEN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

200 Citations (Scopus)


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
Pages (from-to)1408-1432
Number of pages25
JournalSIAM Journal on Scientific Computing
Issue number4
Publication statusPublished - Jan 2003
Externally publishedYes


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


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