Spatially adaptive wavelet thresholding with context modeling for image denoising

Abstract

Abstract-The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the literature has focused on developing the best uniform threshold or best basis selection. However, not much has been done to make the threshold values adaptive to the spatially changing statistics of images. Such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image (such as the identification of smooth or edge regions) to be incorporated into the algorithm. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to changing image characteristics. Each wavelet coefficient is modeled as a random variable of a generalized Gaussian distribution with an unknown parameter. Context modeling is used to estimate the parameter for each coefficient, which is then used to adapt the thresholding strategy. This spatially adaptive thresholding is extended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than the best uniform thresholding with the original image assumed known.

RETRACTED ARTICLE: Document image analysis: issues, comparison of methods and remaining problems

“…Accordingly, promising results are exhibited in the state of the arts based on these approaches (Bharath and Ng 2005;Zhong and Ning 2005;Portilla Zhou et al 2002;Chang et al 2000;Bala and Ertuzun 2002;Choi and Baraniuk 2004).…”

Time-Scale Similarities for Robust Image De-noising

“…PSNR values have been compared with the most recent and powerful de-noising approaches that follow NL-means philosophy. In particular we have selected: the Bayesian non local means and variable window sizes in [13], the image denoising with block matching and 3D filtering BM-3D FFT in [6], the improved NL-means with iterations [32], the PCA based NL means [28], the spatially adaptive wavelet thresholding with context modelling SAWT in [5] (that is very close, in spirit, to NL-means), the SURE based NL-means [31] and the two level adaptation Gaussian mix- Fig. 8 Zoom of the denoised Lena, Barbara, Peppers and Boats images in Fig.…”

“…Nonethe- Table 1 512 × 512 × 8 bits Lena, Barbara, Peppers and Boats images. Comparisons (PSNR) between ANL-means and the denoising approaches in [5,6,12,13,28,31,32,34] less, the similarity measure in (10) gives it the second dimension, since it is able to detect edges as connected curves composed of neighboring and similar time-scale atoms. An example is shown in Fig.…”

“…De-noising is a fascinating and widely investigated topic of image processing, as proved by the significant related literature-see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein. It is often used as an essential preprocessing step in many applications, since it aims at recovering a signal f from its corrupted version g, that is supposed to be…”

Empirical Study of Wavelet Domain Image Joint Statistics and Proposition of an Efficient Correlation Map

“…inter-scale [2,11,18], 2. intra-scale (spatial) [19][20][21][22], and 3. combined intra-and inter-scale [5,7,8,10,23,24].…”