4.A Review of Image Denoising Algorithms, with a New one
A.Buades,B.Coll and J.M. Morel, Multiscale Model. Simul., vol.4, no.2, pp.490 -530, 2005
This paper mainly focuses in comparing the image denoising algorithms with the NLM(Non-Local Means) algorithm, where it not only denoises the image but also preserves the fine details and structures in an image. The performance of the denoised image is also compared based on three criteria such as the method noise, Mean square error and visual quality of the restored image.
A good quality image has a standard deviation of about 60. The effect of noise in a digital image can be measured using standard deviation. Denoising algorithms removes the small details in the image as they are unable to differentiate between noise and fine details. Some others create distortions or artifacts( Blur, ringing,checkerboard,staircase and wavelet outliers ) while denoising the image.
I.Method Noise Comparison:
The following describes the advantages and disadvantages of the denoising algorithms.
Gaussian Filter: It preserves the flat regions of the image and performs poorly near the edges and textures.
Anisotropic Filter: Good preservation of edges and perform poorly in flat regions.
Neighborhood filter: Preserves the flat objects,contours,textures, details and contrasted edges , while edges with low contrast are not kept.
Local adaptive filters in transform domain: A moving window is used to analyse the noisy image. At each position of the window, the spectrum is computed and modified. Later, the inverse transform is used to estimate the value of the centre pixel of the window. Only the center pixel of the restored window is used. This method is called Empirical Wiener Filter (EWF). The edges in the window produce large coefficients , the cancellation of this coefficients will produce oscillations, that results in chessboard patterns.
Wavelet thresholding: There are two procedures available to modify the noisy coefficients.
* Hard Thresholding: cancels the coefficients smaller than the certain threshold. The image is represented in large coefficients which is kept , whereas the noise that is distributed across as small coefficients are cancelled. Edges have small coefficients lower than threshold and so they are removed.This causes wavelet outliers.
* Soft Thresholding: It attenuates all the coefficients to reduce the noise, preserving the structure of the wavelet coefficients and reducing the oscillations near discontinuities.
Translation invariant wavelet thresholding: The wavelet thresholding methods is improved by averaging all the translations of the degraded signal in the inverse form.This method avoids artifacts like staircase and wavelet outliers.
NL-Means Algorithm: All the local smoothing and frequency domain filters aims in noise reduction and reconstruction of the geometrical configuration but fails to preserve the fine structure and details in the image. NL-Means algorithm takes advantage of high degree of redundancy of the image, where every small window in a natural image has many similar windows in the same image. Each pixel value is computed from every other pixel in an image. The weight is chosen based on the similarity(Intensity of grey levels) between the pixels. The similarity between the pixels is measured as a decreasing function of the euclidean distance of the similarity windows.Large euclidean distances lead to nearly zero weights.
II.Visual Quality Comparison: The visual quality of the restored images are compared based on the non presence of the artifacts, reconstruction of edges, textures and fine structures. The Local smoothing filters and local frequency filters are unable to reconstruct the pattern. Only the NL means and global fourier wiener filter reconstruct the original texture.
III.Mean square error comparison: It is the square of the euclidean distance between the original image and its estimate. NL- means MSE is more precise than other algorithms in the presence of periodic and stochastic patterns.
Conclusion: Gaussian convolution preserves only flat zones, while contours and fine structures are removed or blurred. Anisotropic filters preserve straight edges, but flat zones have many artifacts. The NL-Means algorithm automatically takes the advantage of the each mentioned algorithm , thereby reducing the noise and preserving the details of the digital image with good visual quality.
Software: http://www.mathworks.com/matlabcentral/fileexchange/13619-toolbox-non-local-means
A good quality image has a standard deviation of about 60. The effect of noise in a digital image can be measured using standard deviation. Denoising algorithms removes the small details in the image as they are unable to differentiate between noise and fine details. Some others create distortions or artifacts( Blur, ringing,checkerboard,staircase and wavelet outliers ) while denoising the image.
I.Method Noise Comparison:
The following describes the advantages and disadvantages of the denoising algorithms.
Gaussian Filter: It preserves the flat regions of the image and performs poorly near the edges and textures.
Anisotropic Filter: Good preservation of edges and perform poorly in flat regions.
Neighborhood filter: Preserves the flat objects,contours,textures, details and contrasted edges , while edges with low contrast are not kept.
Local adaptive filters in transform domain: A moving window is used to analyse the noisy image. At each position of the window, the spectrum is computed and modified. Later, the inverse transform is used to estimate the value of the centre pixel of the window. Only the center pixel of the restored window is used. This method is called Empirical Wiener Filter (EWF). The edges in the window produce large coefficients , the cancellation of this coefficients will produce oscillations, that results in chessboard patterns.
Wavelet thresholding: There are two procedures available to modify the noisy coefficients.
* Hard Thresholding: cancels the coefficients smaller than the certain threshold. The image is represented in large coefficients which is kept , whereas the noise that is distributed across as small coefficients are cancelled. Edges have small coefficients lower than threshold and so they are removed.This causes wavelet outliers.
* Soft Thresholding: It attenuates all the coefficients to reduce the noise, preserving the structure of the wavelet coefficients and reducing the oscillations near discontinuities.
Translation invariant wavelet thresholding: The wavelet thresholding methods is improved by averaging all the translations of the degraded signal in the inverse form.This method avoids artifacts like staircase and wavelet outliers.
NL-Means Algorithm: All the local smoothing and frequency domain filters aims in noise reduction and reconstruction of the geometrical configuration but fails to preserve the fine structure and details in the image. NL-Means algorithm takes advantage of high degree of redundancy of the image, where every small window in a natural image has many similar windows in the same image. Each pixel value is computed from every other pixel in an image. The weight is chosen based on the similarity(Intensity of grey levels) between the pixels. The similarity between the pixels is measured as a decreasing function of the euclidean distance of the similarity windows.Large euclidean distances lead to nearly zero weights.
II.Visual Quality Comparison: The visual quality of the restored images are compared based on the non presence of the artifacts, reconstruction of edges, textures and fine structures. The Local smoothing filters and local frequency filters are unable to reconstruct the pattern. Only the NL means and global fourier wiener filter reconstruct the original texture.
III.Mean square error comparison: It is the square of the euclidean distance between the original image and its estimate. NL- means MSE is more precise than other algorithms in the presence of periodic and stochastic patterns.
Conclusion: Gaussian convolution preserves only flat zones, while contours and fine structures are removed or blurred. Anisotropic filters preserve straight edges, but flat zones have many artifacts. The NL-Means algorithm automatically takes the advantage of the each mentioned algorithm , thereby reducing the noise and preserving the details of the digital image with good visual quality.
Software: http://www.mathworks.com/matlabcentral/fileexchange/13619-toolbox-non-local-means
Results for MATLAB code
Elapsed time: 0.241640 seconds