PROJECT TITLE 

STUDY AND ANALYSIS OF PERIODICNOISE

REDUCTION ALGORITHM IN FOURIER DOMAIN   

By

1)  Omar Ibrahim Abdoh Ahmed 4318047732) Fahad Saud Hassan Al-Zaidi 431807167

3) Mosa Mohammed Hasan Al-Barqi 4338214094) Hamad Ibrahim Al-Hilaly 4318071225) Ali Mohammed Ibrahim Al- Amri 431806319

  Supervised by:

 Dr. Justin Varghese

(Associate professor)

1. Objectives : 

• To Implement and analyze periodic noise reduction algorithms.

• To Perform Image restoration of Periodic Noise corrupted

Images.

• To make a consolidated software to restore periodic noise

corrupted digital images.

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Why Matlab ?

• MATLAB is a program used for mathematics calculation

• It is also used for image processing

• It makes easy manipulation of images

• It provides built in functions that used for image processing

and makes the programming job easy while testing algorithms

• MATLAB provides an easy environment for programming

• It also provides the Graphical User Interface (GUI)

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Frequency domain Filtering an Example (Idea of the project)

 

• Example:   

Original fft2 for original corrupted fft2 for corrupted apply filter output

Median filter in frequency domain (Aizenburg algorithm-1)[1]

for i= 6:m-5 for j=6:n-5d=sqrt((i-(m/2))^2+sqrt(j-(n/2))^2); if d>20 s=reshape((a(i-5:i+5,j-5:j+5)),1,121); me=median(s); th=abs(a(i,j))/abs(me); if th>2 b(i,j)=me; end end

endend

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Original image Original FFT Corrupted Image

Corrupted FFT Restored FFT Restored Image

Mean filter in frequency domain (Aizenburg algorithm-2) [2]

for i= 6:m-5 for j=6:n-5d=sqrt((i-(m/2))^2+sqrt(j-(n/2))^2); if d>20 s=reshape((a(i-5:i+5,j-5:j+5)),1,121); me=mean(s); th=abs(a(i,j))/abs(me); if th>2 b(i,j)=me; end

end endend

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Original image Original FFT Corrupted image

Corrupted FFT Restored FFT Restored image

Low pass filter in frequency domain (Aizenburg algorithm-3) [3]

for i= 1:m for j=1:n d=sqrt((i-(m/2))^2+(j-(n/2))^2); if (d>rgn) b(i,j)=0; else b(i,j)=a(i,j); end endend end 

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Original image Original FFT Corrupted image

Corrupted FFT Restored FFT Restored image

Gaussian notch filter algorithm [4] for k=-5:5 for l=-5:5 h(6+k,6+l)=1-exp((-0.01)*(k^2+l^2)); endendc=a;the1=a;rgn=45;for i= 6:m-5 for j=6:n-5 d=sqrt((i-(m/2))^2+(j-(n/2))^2); if d>rgn s=reshape((a(i-5:i+5,j-5:j+5)),1,121); med=median(s); the(i,j)=abs(a(i,j))/abs(med); if the(i,j)>7 for k=-5:5 for l=-5:5 c(i+k,j+l)=min([a(i+k,j+l)*h(6+k,6+l) c(i+k,j+l)]); end end end endend end

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Original image Original FFT Corrupted image

Corrupted FFT Restored FFT Restored image

Comparison criteria [5] 1-MAE ( Mean Absolute Error )

 

Compare between the original image and the restored image.

To know the error rate between original image and restored image. Code:

s=0; for i=1:m for j=1:n s=s+abs(o(i,j)-z(i,j)); end end mae = s/(m*n);

 

m n

i 1 j 1

1MAE O i, j Z i, j

mn

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2-MSE ( Mean Square Error )

The MSE is the cumulative square error between the original and restored images and is defined by :

 Code: s=0; for i=1:m for j=1:n s=s+(o(i,j)-z(i,j))^2; end end mse = s/(m*n);

m n

2

i 1 j 1

1MSE O i, j Z i, j

mn

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3-PSNR ( Peak Signal to Noise Ratio )

PSNR is the ratio between maximum possible power of a signal and the

power of distorting noise which affects the quality of its representation. It

is defined by: 

Code:

s=0; for i=1:m for j=1:n s=s+(o(i,j)-z(i,j))^2; end end

mse = s/(m*n); Psnr= 10*log10(255^2/mse)

2

10MSE

255PSNR 10log dB

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4-Time in seconds:

The complexity of all algorithms are of O(n2)

While executing the algorithms in the same computer, algorithm

that finishes its processing in less time is the best .

We determine the execution time of different algorithms in seconds

by the Matlab functions tic and toc

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Menu

Tools GUI

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Conclusion & Future Work

• We Finished the following modules of the project

1. The implementation of Four algorithms used in the comparative study.

2. Designed the GUI.

3. Implemented the Comparison Criteria ( PSNR, MAE, MSE, Computational Time in seconds)

• Future Work

1.To complete the consolidated software.

2. To analyze and compare the algorithms 

References 

[1] Aizenberg, I., Butakoff, C.: Frequency domain median-like filter for periodic and quasi-periodic noise removal. In: SPIE Proceedings of the Image Processing, 4667, pp. 181–191 (2002) [2] Aizenberg, I., Butakoff, C.: Nonlinear frequency domain filter for quasi periodic noise removal. In: Proceeding of International TICSP Workshop on Spectra Methods and Multirate Signal Processing. TICSP Series, 17, pp. 147–153 (2002) [3] Gonzalez, Rafael C., and Richard E. Woods. "Digital image processing." (2002). [4] Aizenberg, Igor, and Constantine Butakoff. "A windowed Gaussian notch filter for quasi-periodic noise removal." Image and Vision Computing 26.10 (2008): 1347-1353. [5] Varghese, Justin, et al. "Efficient adaptive fuzzy-based switching weighted average filter for the restoration of impulse corrupted digital images." Image Processing, IET 8.4 (2014): 199-206.

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Questions ?

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