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A New Adaptive Diffusive Function for Magnetic Resonance Imaging Denoising Based on Pixel Similarity.

Heydari M, Karami MR - J Med Signals Sens (2015 Oct-Dec)

Bottom Line: The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function.Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR).As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Faculty of Electrical and Computer Engineering, Babol University of Technology, Mazandaran, Iran.

ABSTRACT
Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function. This function was first introduced by Perona and Malik (P-M) in their model. They proposed two functions that are most frequently used in PDE-based methods. Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR). In this paper we propose a modified diffusive function with fractional power that is based on pixel similarity to improve P-M model for low SNR. We also will show that our proposed function will stabilize the P-M method. As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR.

No MeSH data available.


Investigation of the instability of Perona and Malik functions for different value of K: (a) gη for Eq. 2, (b) gη for Eq. 3
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Figure 2: Investigation of the instability of Perona and Malik functions for different value of K: (a) gη for Eq. 2, (b) gη for Eq. 3

Mentions: Obviously, gη(/∇u/) = g(/∇u/) in Eq. 17 is always positive which means diffusion forward and making image smooth. However, gξ(/∇u/) = g′(/∇u/)/∇u/+g(/∇u/) can be either positive or negative leading to unstable results, this causes instability of the diffusion process.[272930] Considering P-M functions of Eq. 2 and Eq. 3, it appears that their corresponding gη functions, in the global scheme of Eq. 17, can sometimes takes negative values [Figure 2]. This leads to local instabilities of the P-M's PDE which degrades the processed image instead of denoising it. As shown in Figure 2, g2 is more stable than g1 and for this reason; diffusive function g2 is utilized in this paper.


A New Adaptive Diffusive Function for Magnetic Resonance Imaging Denoising Based on Pixel Similarity.

Heydari M, Karami MR - J Med Signals Sens (2015 Oct-Dec)

Investigation of the instability of Perona and Malik functions for different value of K: (a) gη for Eq. 2, (b) gη for Eq. 3
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759836&req=5

Figure 2: Investigation of the instability of Perona and Malik functions for different value of K: (a) gη for Eq. 2, (b) gη for Eq. 3
Mentions: Obviously, gη(/∇u/) = g(/∇u/) in Eq. 17 is always positive which means diffusion forward and making image smooth. However, gξ(/∇u/) = g′(/∇u/)/∇u/+g(/∇u/) can be either positive or negative leading to unstable results, this causes instability of the diffusion process.[272930] Considering P-M functions of Eq. 2 and Eq. 3, it appears that their corresponding gη functions, in the global scheme of Eq. 17, can sometimes takes negative values [Figure 2]. This leads to local instabilities of the P-M's PDE which degrades the processed image instead of denoising it. As shown in Figure 2, g2 is more stable than g1 and for this reason; diffusive function g2 is utilized in this paper.

Bottom Line: The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function.Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR).As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Faculty of Electrical and Computer Engineering, Babol University of Technology, Mazandaran, Iran.

ABSTRACT
Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function. This function was first introduced by Perona and Malik (P-M) in their model. They proposed two functions that are most frequently used in PDE-based methods. Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR). In this paper we propose a modified diffusive function with fractional power that is based on pixel similarity to improve P-M model for low SNR. We also will show that our proposed function will stabilize the P-M method. As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR.

No MeSH data available.