Research On Image Denoising Approach Based On Wavelet And Its Statistical Characteristics

An image is often and inevitably corrupted by noise in its acquisition or transmission. The noise in an image has degraded severely the following-up image processing tasks, such as image segmentation, coding, feature extraction, and target detection. Thus noise reduction becomes a very important image pre-processing for improving the quality of image and meeting the needs of higher lever processing tasks. The goal of image denoising is to remove the noise while retaining as much as possible the important signal features and details. Generally speaking, it is difficult for traditional image denoising methods to reach a satisfactory trade-off between noise suppression and detail preserving. As an analytic way in time-frequency, wavelet transform is multi-scale and multi-resolution, and provides a new and powerful tool for signal processing. Wavelet has been successfully used in the field of image denoising in the last two decades. Wavelet based denoising has been acknowledged as an important research in image noise reduction and image restoration. Now the focus of the field is transfered to model-based denoising methods, which are mainly depend on statistical characteristics of image wavelet coefficients. The research of denoising theory and ways with respect to wavelet and its statistics is obviously of much significance for both theory and application.Taken wavelet theory as tool, this dissertation gives systematic and deep investigation to theory and approach of image noise reduction in wavelet domain. The main contributions of this thesis are given below.1. Overview of wavelet domain image denoisingA comprehensive study in wavelet based image denoising is addressed in the first two chapters of the thesis, which plays fundamental roles for the whole dissertation. Firstly, the development of image noise suppression, particularly wavelet image denoising, is reviewed. Secondly, as there is no a better way to categorize the existing approaches in the field of wavelet denoising, to our knowledge, this dissertation presents a new classification with wide and deep insight, according to the evolvement of the field. The wavelet denoising methods are categorized into four types, and typical algorithms in each type are analyzed. Thirdly, being commonly viewed as fundamental, wavelet thresholding denoising is elaborately discussed. The threshold selection, which is the most critical issue in thresholding denoising, is clearly explained by combination with the corresponding algorithms. Comprehensive comparative simulations are conducted on various representative methods of wavelet thresholding denoising under orthonormal wavelet basis and shift-invariance wavelet basis, respectively. And some useful conclusions are drawn from the experiment results. In the last, regarding the issue of producing 1-dimension simulation signals, a new method is proposed under strict theory deduction to produce noisy signals with high SNR accuracy.2. Wiener filtering in wavelet domainWiener filtering in wavelet domain is a very active branch in the field of wavelet image denoising. Three forms are defined for wavelet based Wiener filtering and correspondingly three new denoising methods are developed. The first is an iterative algorithm for Wiener filtering in wavelet domain. On the basis of empirical Wiener filter, BayesShrink method is adopted to increase accuracy of the expected signals, and multiple wavelet bases were selected properly to uniquely capture some signal characteristics. This iterative method has effectively improved the denoising performance. The second is a joint scheme, which is implemented by BayesShrink algorithm to obtain a pre-denoised image, followed by spatial Lee filtering. The crux of the joint scheme lies in the simple yet effective estimation of the nearly optimal noise variance for Lee filter, and thus the matching between two denoising algorithms in different domains is ensured. Finally, a locally adaptive wavelet domain Wiener filter is proposed. By theoretically analyzing the expected error of Mihcak's LAWML algorithm, a threshold for local variance estimation of observed wavelet coefficients is derived. Experiment results demonstrate that compared with LAWML algorithm, the presented locally adaptive method has improved the accuracy of variance estimation, and yielded better denoising performance in terms of objective PSNR and subjective visual effect.3. Research on image denoising based on statistical model of wavelet coefficientsThis dissertation has studied Bayesian wavelet domain denoising approach which is based on characteristics of image wavelet coefficients and improved two famous existing algorithms by pointing out some drawback of them. For Sendur's bivariate model based denoising algorithm, the coefficients of three highest frequency sub-bands, which remain unaltered in Sendur's original paper, are modified by MAP soft thresholding rule via locally adaptive fashion. For Moulin's subband adaptive MapShrink algorithm, a new stochastic model is presented. In our model, each coefficient in a subband is assumed to be Laplacian with different marginal standard deviation which can be estimated from a local neighborhood. In this way, a locally adaptive MapShrink threshold is obtained.This thesis has also developed two algorithms by introducing classification of wavelet coefficients into noise suppression. In the first method, a pixel-adaptive Gaussian mixture model is proposed. Wavelet coefficients were classified into two categories using local Bayesian threshold, and the model parameters such as large and small variances, related probabilities, could be estimated from the information of the two classified coefficients in a neighbouring window. Then Wiener filter is designed according to Minimum Mean Squared Error (MMSE) criterion. The second method extends the neighbouring threshold of wavelet coefficients from 1-D signal to 2-D image case. Each coefficient in a subband is classified as"large"or"small"category, according to its corresponding neighbouring threshold. Those"small"coefficients are set to zero, whereas those"large"coefficients are modeled as zero-mean Gaussian random variables with high local correlation. Simulation results show this algorithm has the advantages of both low computational demands and effective denoising performance.4. Speckle reduction for SAR images using wavelet statistical modelAs a practical example of image denoising, the last part of the thesis covers a specific application of wavelet denoising in SAR image despeckling. The approaches of SAR image speckle suppression, particularly those based on wavelet statistical model, are investigated firstly. A novel locally adaptive speckle filtering is proposed based on Bayesian MAP estimation in wavelet domain. In this method, logarithmically transform is applied to original speckled SAR image, followed by redundant wavelet transform. The proposed method uses the Rayleigh distribution for speckle noise and a Laplacian distribution for modelling the statistics of wavelet coefficients due to signal. A Bayesian estimator with analytical formula is derived from MAP estimation, and the resulting formula is proven to be equivalent to soft thresholding in nature which makes algorithm very simple. In order to exploit the correlation among wavelet coefficients, the parameters of Laplacian model are assumed to be spatially correlated and can be computed from the coefficients in a neighboring window, thus making our method spatially adaptive in wavelet domain. Theoretical analysis and simulation experiment results show that this proposed method can effectively suppress speckle noise in SAR images while preserving as much as possible important signal features and details.