Multichannel restoration of single channel images using a wavelet decomposition

  • Authors:

  • Mark R. Banham;Hector Gonzalez;Nikolas P. Galatsanos;Aggelos K. Katsaggelos

  • Affiliations:

  • Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL;Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL;Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL;Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
  • Year:
  • 1993

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Abstract

In this paper, multichannel linear filtering is applied to the restoration of single channel images through the use of a wavelet decomposition. A new matrix structure for the separable 2-D wavelet transform is present.ed which allows the transformation of block circulant operators, found in 2-D linear filtering problems, into semi- block circulant operators, which are defined here. These operators are easily treated as block diagonal matrices in the wavelet-frequency domain. An adaptive Wiener filter is implemented in this domain, which utilizes the cross correlations between subbands in the decomposition to subst antially improve the restoration of noisy-blurred images over that found with single channel filtering. This improvement is especially evident when the power spectrum of the original image is available.