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Title: Denoising by singularity detection
Authors: Hsung, TC
Lun, PKD 
Siu, WC 
Keywords: Tomographic image reconstruction
Wavelet transform
Wavelet coefficients
Image denoising
Issue Date: Nov-1999
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on signal processing, Nov. 1999, v. 47, no. 11, p.3139-3144 How to cite?
Journal: IEEE transactions on signal processing 
Abstract: In this correspondence, a new algorithm for noise reduction using the wavelet transform is proposed. Similar to Mallat's wavelet transform modulus maxima denoising approach, we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales. However, we do not perform maxima detection and processing; therefore, complicated reconstruction is avoided. Instead, the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding “cone of influence,” and the coefficients that correspond to the regular part of the signal for reconstruction are selected. The algorithm gives an improved denoising result, as compared with the previous approaches, in terms of mean squared error and visual quality. The new denoising algorithm is also invariant to translation. It does not introduce spurious oscillations and requires very little a priori information of the signal or noise. Besides, we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so-called “directional cone of influence.” The denoising technique is applied to tomographic image reconstruction, where the improved performance of the new approach can clearly be observed.
ISSN: 1053-587X
EISSN: 1941-0476
DOI: 10.1109/78.796450
Rights: © 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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