Wavelet-based deconvolution using optimally regularized inversion for ill-conditioned systems

Ramesh Neelamani; Hyeokho Choi; Richard G. Baraniuk

doi:10.1117/12.366812

26 October 1999 Wavelet-based deconvolution using optimally regularized inversion for ill-conditioned systems

Ramesh Neelamani, Hyeokho Choi, Richard G. Baraniuk

Author Affiliations +

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366812
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

We propose a hybrid approach to wavelet-based 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 in non-invertible. Using a mean-square-error (MSE) metric, we strike an optimal balance between Fourier-domain regularization (matched to the system) and wavelet-domain regularization (matched to the signal/image). Theoretical analysis reveals that the optimal balance is determined by the economics of the signal representation in the wavelet domain and the operator structure. The resulting algorithm is fast (O(Nlog²₂N) complexity for signals/images of N samples) and is well-suited to data with spatially-localized phenomena such as edges. In addition to enjoying asymptotically optimal rates of error decay for certain systems, the algorithm also achieves excellent performance at fixed data lengths. In simulations with real data, the algorithm outperforms the conventional time-invariant Wiener filter and other wavelet- based deconvolution algorithms in terms of both MSE performance and visual quality.

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Ramesh Neelamani, Hyeokho Choi, and Richard G. Baraniuk "Wavelet-based deconvolution using optimally regularized inversion for ill-conditioned systems", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366812

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