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Wavelet-based image denoising algorithm under overcomplete expansion

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Description

There has been growing interest of wavelet-based denoising schemes for removing additive white Gaussian noise from corrupted images recently. Such popularity is mainly due to that wavelet provides an appropriate basis for separating noise signal from image signal.

Important features in images(e.g. edges) are usually represented by large coefficients, thus facilitating their separation from noise components which usually correspond to small coefficients in wavelet domain. Even ad-hoc thresholding strategy generates satisfactory denoising result and often outperforms other class of denoising schemes such as nonlinear filtering or nonlinear diffusion in terms of objective performance (MSE or PSNR).

We present a new image denoising scheme using overcomplete expansion in this project . The overcomplete expansion is obtained in a similar fashion as Translation-Invariant (TI) denoising [1] by shifting original signal. But unlike [1] processing shifted versions separately, we propose to put them together for the reason of achieving more accurate statistical models for signal components. The highband coefficients are viewed as the mixture of non-edge coefficients observing a zero-mean model and edge coefficients observing a biased-mean model. The optimal noise suppression strategies (MMSE estimation) are derived for both edge and non-edge coefficients. For edge coefficients whose true bias is not available, an approximated solution based on Least-Square estimation and directional filtering is adopted.
The new denoising algorithm appears to give smaller MSE results than almost all recently-published results in the literature of wavelet denoising.

 

[1] R.R. Coifman and D.L. Donoho, “Translation-Invariant denoising“, Wavelets and Staristics, Springer-Verlag Lecture Notes, 1995

Wavelet thresholding

2D dyanic wavelet transform

 

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