Noise Reduction Image Restoration

Gaussian Noise : Matlab

t_gaus = imnoise (t, ‘gaussian’); imshow(t_gaus);

Salt and Pepper Noise :

MATLAB

t_sp = imnoise (t, ‘salt & pepper’); imshow(t_sp);

Other Additive Noise Models

•

_{Rayleigh Noise}

•

_{Gamma(Erlang) Noise}

•

_{Exponential Noise}

•

_{Uniform Noise}

•

_{Impulse Noise}

Periodic Noise

Noise components

Are generated due to electrical or electromechanical interference during image acquisition

Periodic Noise : MATLAB

tw = imread(filename); t = rgb2gray(tw);

s = size(t);

[x,y] = meshgrid(1:s(1), 1:s(2)); p = sin(x/3+y/5)+1;

t_pn = (im2double(t)+p’/2)/2; imshow(t_pn);

10 13 5

11 20 15

8 0 0

Rank-Order Filter

• _{Sort the intensities within the mask.}

• _{Choose the intensity at i}th position as output.

10 20 10 15 5

Sort intensity

Median filter

Min. filter

Rank-Order Filter

Rank-Order Filter :

Max Filter

• _{Output pixel is the maximum intensity of the pixels within the} mask. (find brightest point)

BEFORE AFTER

Rank-Order Filter :

Min Filter

• _{Output pixel is the minimum intensity of the pixels within the} mask. (find darkest point)

BEFORE AFTER

Rank-Order Filter : Median

Filter

-- Repeated passes of median filter tend to blur the image. -- Keep the number of passes

• _{Output pixel is the}

mid-intensity of the pixels within the mask (the median

intensity).

• _{Adaptive median filter}

memiliki tujuan ganda yaitu

menghapus impuls noise

pada gambar dan

mengurangi distorsi pada gambar.

Rank-Order Filter : Median

Filter

BEFORE AFTER

Rank-Order Filtering:

MATLAB

• _Command: ordfilt2

• _Syntax: ordfilt2(image, order, domain); medfilt2(image);

• image _{: input image}

• order _{: which order of the sorted intensity (minimum to}

maximum value) taken as output

• domain : matrix indicating the neighborhood. 1 : pixels in the neighbor.

0 : pixels not in the neighbor E.g. cmin = ordfilt2(image, 1, ones(3,3));

Mean Filters

Mean Filters

Mean Filter

Good Results of Geometric Mean Filter

BEFORE AFTER

Mean Filter :

Bad Results of Geometric Mean Filter

BEFORE AFTER

Mean Filters

Mean Filters

Mean Filters

Good Results of Contraharmonic Mean Filter

Mean Filters

Bad Results of Contraharmonic Mean Filter

• _{Arithmetic mean filter and geometric mean filter are well suited for}

random noise such as Gaussian noise

• _{Contraharmonic mean filter is well suited for impulse noise}

Order-statistic Filters

Alpha-Trimmed Mean Filter

• _{Output is the mean of the data after removing the first d/2} and the last d/2 ordered data.

10 13 5 1 from the bottom.)

Order-statistic Filters

Effect of Alpha-Trimmed Mean Filter

BEFORE AFTER

Image corrupted by salt-and-pepper

-High level of noise  large filter

-Median and

alpha-trimmed filter performed better

Periodic Noise Reduction

Frequency Domain Filtering



Band Reject Filters

(Selective

Filter)

• _{Ideal Band-Reject Filters}

Periodic Noise Reduction

Frequency Domain Filtering



Band Reject Filters

• _{Butterworth Band-Reject Filter of Order n}

• _{Gaussian and-Reject Filter}

Periodic Noise Reduction

Periodic Noise Reduction

Frequency Domain Filtering



Band Pass Filters

• _{Opposite operation of a band-reject filter}

1

( , )

bp

br

Periodic Noise Reduction

Frequency Domain Filtering



Notch Filters

• _{Rejects (or passes) frequencies in predefined neighborhoods} about a center frequency

Ideal

Butterworth

Gaussian

Must appear in

Periodic Noise Reduction

Frequency Domain Filtering



Notch Filters

• _{Ideal Notch Filters}

1 0 2 0

Horizontal lines of the noise pattern I can be seen

Tugas

• _{Cari tahu bagaimana cara menghilangkan periodic noise} menggunakan band-reject filter, band-pass filter atau notch filter pada MATLAB.