Denoising of Poisson-Distributed Data by Wavelet Decompositon

Many important problems in engineering and science are well-modeled by Poisson processes. A common technique for noise reduction is to use a filter. Wiener filter, which utilizes the second-order statistics of the Fourier decomposition, and the median filter which is based on the theory of order statistion, are normally used to denoise degraded images. Wavelet-based methods are powerful tools for image denoising and have been used in various applications. In recent years, a new method based on wavelet decomposition which is called ”BayesShrinkage”[1][3] has gained considerable attention in the wavelet domain. Filter processing is faulty due to in denoising by germinating lags. Wavelet shrinkage is a fast nonlinear method for discontinuity-preserving image denoising. It is based on the idea of decomposing an image on a wavelet basis, shrinking all coefficients with small magnitude, and reconstructing the filtered image from the shrunken coefficients. The success of this procedure is based on the assumption that the original image can be represented by a relatively small number of wavelet coefficients with large magnitude, while moderate Poisson noise affects all coefficients, although to a less severe amount. But Bayesshrinkage is just effective for small-amplitude noise coefficients, not for large-amplitude noise coefficients exceed the thresholding value. Usually, only the wavelet coefficients are thresholded, the approximation coefficients have been kept. However, the approximation coefficients are also noisy, especially when the noise is large. In the present paper we address this problem by proposing a new method of reducing small and large-amplitude noise using a thresholding process of wavelet decomposition coefficients and using DACWMF(Directional Adaptive Center Weighted Median Filter)for large noise coefficients. This paper is organized as follows. Section 2 provides a brief introduction to thresholding for approximation and wavelet coefficients and large noise reduction using DACWMF. In Section 3, we describe our simulation and results on experiment data from conventional and proposed methods. The paper is concluded with a summary in Section 4. 2. Proposed Method