Wavelet-domain regularized deconvolution for ill-conditioned systems

Ramesh Neelamani, Hyeokho Choi, Richard Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations

Abstract

We propose a hybrid approach to wavelet-based image deconvolution that comprises Fourier-domain system inversion followed by wavelet-domain noise suppression. In contrast to conventional wavelet-based deconvolution approaches, the algorithm employs a regularized inverse filter, which allows it to operate even when the system is non-invertible. Using a mean-square-error metric, we strike an optimal balance between Fourier-domain regularization that is matched to the system and wavelet-domain regularization that is matched to the signal. Theoretical analysis reveals that the optimal balance is determined by economics of the input signal wavelet representation and the operator structure. The resultant algorithm is fast, O(N log2 2 N) where N denotes the number of samples, and is well-suited to data with spatially-localized phenomena such as edges. In addition to enjoying asymptotically near-optimal rates of error decay for some systems, the algorithm also achieves excellent performance at fixed data lengths. In simulations with real data, the algorithm outperforms the conventional LTI Wiener filter and other wavelet-based deconvolution algorithms in terms of both visual quality and MSE performance.

Original languageEnglish
Title of host publicationIEEE International Conference on Image Processing
Place of PublicationLos Alamitos, CA, United States
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages204-208
Number of pages5
Volume1
StatePublished - Dec 1 1999
EventInternational Conference on Image Processing (ICIP'99) - Kobe, Jpn
Duration: Oct 24 1999Oct 28 1999

Other

OtherInternational Conference on Image Processing (ICIP'99)
CityKobe, Jpn
Period10/24/9910/28/99

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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