空間 컨벌루션 및 웨이브렛 變換을 利用한 變形된 2次元 디지털 필터에 관한 硏究

Abstract

The denoising of an image corrupted by Gaussian noise is a long established problem in signal or image processing. The corruption of image by noise is common during its acquisition or transmission. The noise has degraded severly the following-up image processing tasks, such as image segmentation, feature extraction, and target detection. Thus denoising becomes a very important image pre-processing for improving the quality of image and meeting the needs of higher lever processing tasks. The aim of denoising is to remove the noise while keeping the signal features as much as possible. Therefore, a number of researches to remove AWGN(additive white Gaussian noise) have been proposed. Traditional algorithms, such as the MF(mean filter), GF(Gaussian filter), SDWF(spatial domain wiener filter), SMF(standard median filter) and CWMF(center weighted median filter) perform image denoising in the spatial domain. However, it is difficult for these traditional spatial denoising methods to reach a satisfactory trade-off between noise suppression and detail preserving. They also smoothing images too much that they blurring the images. In recent years, wavelet transform based image denoising algorithms have shown remarkable success. Donoho and Johnstone presented a method named wavelet shrinkage, and showed its obvious efficiency for signal denoising and inverse problem solving. There are many kinds of denoising methods which based on wavelet transform, such as VisuShrink, SureShrink and BiShrink. However, because wavelet threshold has a natural defect on removing noise and keeping the edge detail, which can not propose a threshold method can perfectly valid information will be separated from the noise and image. So traditional thresholding methods can not simultaneously achieve and maintain the edge information and happen errors when they reconstruct image. In this thesis, a modified spatial domain filter algorithm, a wavelet based scale adaptive thresholding algorithm, and the mixed filter algorithm which connects spatial and wavelet domain algorithm in parallel are proposed to restore image in AWGN. The proposed spatial domain algorithm(proposed algorithm 1) first calculates the value by weighted filter combined by spatial weight and self adaptive mean weight, it can work as low pass filter. Then the proposed algorithm adds the value computed by the equation considering variance of mask and the estimated noise variance as the output value. So it can reduce the blurring. And the wavelet based adaptive thresholding method(proposed algorithm 2) computes the threshold adaptively based on the scale level and estimates wavelet coefficients by using a modified thresholding functions. In the coarsest scale using the advanced thresholding function using a polynomial expression, and the other scales, using the thresholding function considering the dependency between the parent coefficient and child coefficient. This proposed algorithm outperforms on preserving edge information. In a mixed filter algorithm, we connected the spatial domain proposed algorithm 1 and wavelet domain proposed algorithm 2 in parallel to get the restored image with good visual quality.