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Removal of Impulse Noise in Images by Means of the Use of Support Vector Machines

H. Gómez-Moreno, S. Maldonado-Bascón, F. López-Ferreras, and P. Gil-Jiménez

Departamento de Teoría de la Señal y Comunicaciones.Universidad de Alcalá.

SPAIN

IWANN 2003

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Presentation of the problem

Due to a noisy transmission channel or to imperfections in the sensor that records the images , an impulse noise appears.

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There are several methods for the recuperation of this noisy images:

1) Median Filter.

State of the art

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

Ordered values of the pixels included in a 3x3 window

Reconstruction Value

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State of the art

Application of the 3x3 median filter

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State of the art

2) SD-ROM.

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

Ordered values of the pixels inside a 3x3 window.

If the questioned pixel is far away from the central pixel it is a noisy pixel. Then it is changed.

Ordered values of the pixels inside a 3x3 window excluding the central pixel.

The reconstruction value is the mean value of the central pixels.

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State of the art

Application of the SD-ROM method

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Support Vector Machines (SVMs)

We present an algorithm for impulse noise reduction based on the use of Support Vector Machines (SVMs).

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Application of SVMs to noise reduction

1) We use the SVMs for two tasks:a) Classify the pixels between noisy and not

noisy.

b) Obtain the reconstruction value by means of the SVMs regression.

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Application of SVMs to noise reduction

2) Classification. Training.

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

1 1 13 13 2 57 57 49 35 1 12 0 8 9 10 11 44 13 46 -1 6 11 56 4 1 6 12 7 77 -1

... ... 5 8 1 2 1 60 60 53 21

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In the training the values and the support vectors are obtained.

This training is made by minimizing the distance between the decision frontier and the data. In the non linear case it is made in the feature space (non linear transformation).

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Application of SVMs to noise reduction

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

10 21 23 3 26 7 7 9 12 2 10 18 19 0 1 24 23 35 16 1 6 54 21 16 2 27 67

... 0 58 41 32 21 0 0 3 91

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If the value of f(x) is positive there is noise, if it is negative there is no noise.

3) Application of the classification.

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Application of SVMs to noise reduction

4) Regression. Training.

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

1 1 13 13 57 57 49 35 25 12 0 8 9 11 44 13 46 33 6 11 56 4 6 12 7 77 46

... ... 5 8 1 2 60 60 53 21

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Values of the original image

In this case the central pixel is not used.

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Application of SVMs to noise reduction

5) Regression. Application.

x-1,y-1 x-1,y x-1,y+1

x,y-1 x,y x,y+1

x+1,y-1 x+1,y x+1,y+1

1 1 13 13 57 57 49 35 12 0 8 9 11 44 13 46 6 11 56 4 6 12 7 77

... 5 8 1 2 60 60 53 21

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Approximated values

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Results

Noisy Image 20% Reconstructed image

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Results

Image 50% noisy Reconstructed image

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Results

Image 20% noisy Reconstructed image 30% training

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Results

Image 20% noisy Reconstructed image 40% training

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Results

Albert Peppers 20% 30% 40% 50% 20% 30% 40% 50%

SDROM [1] 30.6 28.61 26.66 24.46 31.44 29.3 26.94 24.42 Median 3x3 27.11 23.13 18.95 15.3 29.05 23.84 18.94 15.17 Median 5x5 26.6 25.93 24.77 22.47 30 28.53 26.58 23.57 SVM Median 30% training 33.9 31.35 28.7 26.62 37.68 33.95 28.26 23.57 SVM 30% training 29 27.51 26.83 25.83 38.81 36.32 34.05 31.71 SVM 40% training 32.77 30.27 29.27 27.91 38.35 36.08 34.27 32.15

PSNR results using different methods