A study of orthonormal multi-wavelets
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
Image denoising using neighbouring wavelet coefficients
Integrated Computer-Aided Engineering
Data-driven and optimal denoising of a signal and recovery of its derivative using multiwavelets
IEEE Transactions on Signal Processing
Spatially adaptive wavelet thresholding with context modeling for image denoising
IEEE Transactions on Image Processing
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In this work, we consider a statistically based multiwavelet thresholding method which acts on the empirical wavelet coefficients in groups, rather than individually, in order to obtain an edge-preserving image denoising technique. Our strategy allows us to exploit the dependencies between neighboring coefficients to make a simultaneous thresholding decision, so that estimation accuracy is increased. By interpreting the multiwavelet analysis in a statistical context, we propose a new weighted multiwavelet matrix thresholding rule, based on the statistical modeling of empirical coefficients. This allows the thresholding decision to be adapted to the local structure of the underlying image, hence producing edge-preserving denoising. Extensive numerical results are presented showing the performance of our denoising procedure.