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Wavelet denoising by recursive cycle spinning

Wavelet denoising by recursive cycle spinning,10.1109/ICIP.2002.1040090,Alyson K. Fletcher,Vivek K. Goyal,Kannan Ramchandran

Wavelet denoising by recursive cycle spinning   (Citations: 10)
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Coupling the periodic time-invariance of the wavelet transform with the view of thresholding as a projection yields a simple, re- cursive, wavelet-based technique for denoising signals. Estimating a signal from a noise-corrupted observation is a fundamental prob- lem of signal processing which has been addressed via many tech- niques. Previously, Coifman and Donoho introduced cycle spin- ning, a technique estimating the true signal as the linear average of individual estimates derived from wavelet-thresholded translated versions of the noisy signal. Here, it is demonstrated that such an average can be dramatically improved upon. The proposed algo- rithm recursively "cycle spins" by repeatedly translating and de- noising the input via basic wavelet denoising and then translating back; at each iteration, the output of the previous iteration is used as input. Exploiting the convergence properties of projections, the proposed algorithm can be regarded as a sequence of denoising projections that converge to the projection of the original noisy signal to a small subspace containing the true signal. It is proven that the algorithm is guaranteed to globally converge, and simula- tions on piecewise polynomial signals show marked improvement over both basic wavelet thresholding and standard cycle spinning.
Conference: International Conference on Image Processing - ICIP , vol. 2, pp. 873-876, 2002
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