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Hyperanalytic denoising
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DOI：10.1109/TIP.2007.896633.png)
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Abstract
En 中文
A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of replicates of the image. The replicates are calculated by extending the image into a vector-valued hyperanalytic signal. More than one hyperanalytic signal may be chosen, and either the hypercomplex or Riesz transforms are used, to calculate this object. The deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal, at a fixed scale and position index, are determined. A universal threshold is calculated for the proposed procedure. An expression for the risk of an individual coefficient is derived. The risk is calculated explicitly when the universal threshold is used and is shown to be less than the risk of universal hard thresholding, under certain conditions. The proposed method is implemented and the derived theoretical risk reductions substantiated.
Keywords:
Hilbert transform
image denoising
2-D analytic
wavelets
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