## 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 is 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(N log
_{2}
^{2} N) 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.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Publisher | Society of Photo-Optical Instrumentation Engineers |

Pages | 58-72 |

Number of pages | 15 |

Volume | 3813 |

State | Published - 1999 |

Event | Proceedings of the 1999 Wavelet Applications in Signal and Image Processing VII - Denver, CO, USA Duration: Jul 19 1999 → Jul 23 1999 |

### Other

Other | Proceedings of the 1999 Wavelet Applications in Signal and Image Processing VII |
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City | Denver, CO, USA |

Period | 7/19/99 → 7/23/99 |

## ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics