An adaptive bandwidth nonlocal means image denoising in wavelet domain

EURASIP Journal on Image and Video Processing, Dec 2013

This paper proposes a new wavelet domain denoising algorithm. In the results of conventional wavelet domain denoising methods, ringing artifacts or wavelet-shaped noises are sometimes observed due to thresholding of small but important coefficients or due to generation of large coefficients in flat areas. In this paper, nonlocal means filtering is applied to each subband of wavelet decomposition, which can keep small coefficients and does not generate unwanted large coefficients. Since the performance of nonlocal means filtering depends on the appropriate kernel bandwidth, we also propose a method to find global and local kernel bandwidth for each subband. In comparison with conventional methods, the proposed method shows lower PSNR than BM3D when pseudo white Gaussian noise is added, but higher PSNR than the spatial nonlocal means filtering and wavelet thresholding methods. For the mixture noise or Poisson noise, which may better explain the real noise from camera sensors, the proposed method shows better or comparable results than the state-of-the-art methods. Also, it is believed that the proposed method shows better subjective quality for the noisy images captured in the low-illumination conditions.

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An adaptive bandwidth nonlocal means image denoising in wavelet domain

EURASIP Journal on Image and Video Processing An adaptive bandwidth nonlocal means image denoising in wavelet domain Su Jeong You 0 Nam Ik Cho 0 0 Department of Electrical and Computer Engineering, INMC, Seoul National University , Gwanak-ro, Gwanak-gu, Seoul, 151-744 , Korea This paper proposes a new wavelet domain denoising algorithm. In the results of conventional wavelet domain denoising methods, ringing artifacts or wavelet-shaped noises are sometimes observed due to thresholding of small but important coefficients or due to generation of large coefficients in flat areas. In this paper, nonlocal means filtering is applied to each subband of wavelet decomposition, which can keep small coefficients and does not generate unwanted large coefficients. Since the performance of nonlocal means filtering depends on the appropriate kernel bandwidth, we also propose a method to find global and local kernel bandwidth for each subband. In comparison with conventional methods, the proposed method shows lower PSNR than BM3D when pseudo white Gaussian noise is added, but higher PSNR than the spatial nonlocal means filtering and wavelet thresholding methods. For the mixture noise or Poisson noise, which may better explain the real noise from camera sensors, the proposed method shows better or comparable results than the state-of-the-art methods. Also, it is believed that the proposed method shows better subjective quality for the noisy images captured in the low-illumination conditions. Introduction Denoising is one of the fundamental image processing problems and thus has been studied for a long time. To name a few of the existing methods that are related with our work and the state-of-the-art methods, there are wavelet shrinkage methods [ 1,2 ], a total variation minimization [3], a prior probability modeling [ 4 ], nonlocal means filtering [ 5 ], and BM3D [ 6 ]. Among these, the BM3D generally shows the highest PSNR when the noise is additive white Gaussian. In the case of wavelet domain thresholding methods [ 1,2 ], an image is transformed into the wavelet domain, and the coefficients in each subband are suppressed by hard or soft thresholding. The advantage of wavelet shrinkage methods is that they require not much computations while providing pleasing results. The probabilistic wavelet coefficient modeling method [4] fits the neighborhoods of coefficients as Gaussian scale mixture (GSM) model and applies the Bayesian least squares (BLS) technique to adjust the coefficients. Although wavelet shrinkage methods and BLS-GSM provide relatively high PSNR improvement, shrinking or modifying wavelet coefficients sometimes bring ringing or wavelet-shaped artifacts. For example, wavelet transformation of a step edge generates small coefficients up to the highest subbands. Hence, when the small coefficients are removed by thresholding and are inverse transformed, then ringing artifacts arise due to the loss of high frequencies. In the case of probabilistic wavelet coefficient modeling, unwanted coefficients can be generated in the homogeneous region, which result in wavelet-shaped artifacts in the spatial domain. Another popular denoising method is the nonlocal means filtering [ 5 ], which substitutes a noisy pixel by the weighted sum of neighborhood pixels. The weights are determined based on the kernel density estimation, which can be regarded as a Nadaraya-Watson estimator, i.e., a kind of local constant regression [ 7 ]. In other words, the smooth kernel estimate in the nonlocal means approach is a sum of bumps placed on the data points. The kernel function determines the shape of the bumps, and the ‘smoothing parameter’ or ‘bandwidth’ controls the degree of smoothness. In [ 8 ], an automatic bandwidth selection method was proposed based on the reduction of entropy of image patterns, and the global bandwidth was applied to the overall area of image. However, it is noted that narrower kernels are suitable for the complex regions, whereas larger kernels would be better for more sparse areas. Hence, it is important to find an appropriate bandwidth according to the local characteristics, which is not an easy task. One of the main factors that strongly influence the local properties of the image is the noise statistics in the neighborhood, and thus, the bandwidth needs to be adaptively determined according to the local noise variance. In summary, we need to estimate the local noise statistics for finding an appropriate bandwidth for the given region. There are many methods for estimating the variance of white additive noise in images, but they cannot be used for the images with non-uniform noise variance. In this consideration, the estimation of local noise statistics is necessary to find the appropriate bandwidth for the given area. In this paper, inspired by the performance of nonlocal means filtering method in keeping the structures of the image while suppressing the noise, we attempt to apply the n (...truncated)


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Su Jeong You, Nam Ik Cho. An adaptive bandwidth nonlocal means image denoising in wavelet domain, EURASIP Journal on Image and Video Processing, 2013, pp. 60, Volume 2013, Issue 1, DOI: 10.1186/1687-5281-2013-60