Noise in 8-bit images - MATLAB

Noise is a negative phenomenon that affects a wide variety of digital products. Images, audio or video recordings (digitized). The aim of this article is to point out the effect of noise that can alter the values of individual bits of pixels. As a result, by modifying the most significant bit - the so-called bit. MSB (Most Significant Bit) comes up to 50% of the bit brightness value. Noise thus manifests as a component that darkens the pixel.

Each pixel is made up of eight bits in the case of a black and white image. The higher the bit value, the lighter the bit. Eight bits can result in a value of 0 - 255. For a clearer representation also serve the table:
BIT - bit order
ENCOURAGES VALUE

1 (LSB)	2	3	4	5	6	7	8 (MSB)
0/1	0/2	0/4	0/8	0/16	0/32	0/64	0/128

The implementation in MATLAB represents physical images by loading them into matrices, each image is 512x512px. Each image is thus represented by 262,144 pixels. Each pixel is made up of eight bits, so the image is represented in memory by 2 097 152 binary values. Values ​​are hierarchically ordered from LSB (Less Significant Bit) to MSB (left to right).

The implementation also generates noise that is applied to the loaded image. Noise is generated through a "true random generator" that is based on time, ie (non) periodically. By default, the generation function is periodic with default values ​​from which the number / string is generated. Noise is applied to the original image in columns, which means that noise is applied sequentially to the 1st bit (LSB), 2nd bit, 3rd bit, 4th bit, 5th bit, 6th bit, 7th bit, 8 .bit (MSB). As a result, intermediate results can be saved and plotted in the user representation window.

In order to render the edited images separately after editing each column, they are simply "re-assembled" through the columns of the original (unmodified) image with the edited column. This allows us to render individual images with the column just being edited. The resulting noise image for all columns is stacked from the modified columns. It is apparent from the output that the noise was most affected by the 8th bit (MSB) and 7th bit. At the 1st (LSB) bit, the bit change by noise is not apparent.

Working with black and white pictures is easier, as there is only one color palette. With RGB there are up to 3 color palettes, each pixel being represented by up to 24 bits. Such an implementation would represent 262,144 pixels for an image with 6,291,456 binary values.

The implementation uses 3 images, adding the same noise to all three images. Images are loaded at the beginning of the program by the imread () function with their name. Direct name is their location in the same folder as the program. Mathematically, the program also expresses the peak signal-to-noise ratio (PSNR) and determines the mean quadratic error (MSE).

Used images (save as 8-bit .bmp)!

lena512g.bmp

barbara512g.bmp

girlface512g.bmp

Program:

%%Autor: Bc. Martin Chlebovec
%%E-mail: martinius96@gmail.com
%%Donate: https://paypal.me/chlebovec
%%vymaz figure a premenne
clear all;
close all;
rng shuffle;
%%nacitaj obrazky
obrazok1 = imread('lena512g.bmp');
obrazok2 = imread('barbara512g.bmp');
obrazok3 = imread('girlface512g.bmp');
%%Vygeeneruj maticu
generuj_maticu = uint8(randi([0 1],512*512,1));
%%konverzia dec to bin
bityo1 = de2bi(obrazok1);
bityo2 = de2bi(obrazok2);
bityo3 = de2bi(obrazok3);
%%rozlozenie prveho obrazku
osmystlpec1 = bityo1(:,8); %%MSB
siedmystlpec1 = bityo1(:,7);
siestystlpec1 = bityo1(:,6);
piatystlpec1 = bityo1(:,5);
stvrtystlpec1 = bityo1(:,4);
tretistlpec1 = bityo1(:,3);
druhystlpec1 = bityo1(:,2);
prvystlpec1 = bityo1(:,1);%%LSB
%%rozlozenie druheho obrazku
osmystlpec2 = bityo2(:,8);%%MSB
siedmystlpec2 = bityo2(:,7);
siestystlpec2 = bityo2(:,6);
piatystlpec2 = bityo2(:,5);
stvrtystlpec2 = bityo2(:,4);
tretistlpec2 = bityo2(:,3);
druhystlpec2 = bityo2(:,2);
prvystlpec2= bityo2(:,1);%%LSB
%%rozlozenie tretieho obrazku
osmystlpec3 = bityo3(:,8);%%MSB
siedmystlpec3 = bityo3(:,7);
siestystlpec3 = bityo3(:,6);
piatystlpec3 = bityo3(:,5);
stvrtystlpec3 = bityo3(:,4);
tretistlpec3 = bityo3(:,3);
druhystlpec3 = bityo3(:,2);
prvystlpec3= bityo3(:,1);%%LSB
%%pridanie sumu prvy obrazok
upravenyosmystlpeco1 = osmystlpec1.*generuj_maticu;
upravenysiedmystlpeco1 = siedmystlpec1.*generuj_maticu;
upravenysiestystlpeco1 = siestystlpec1.*generuj_maticu;
upravenypiatystlpeco1 = piatystlpec1.*generuj_maticu;
upravenystvrtystlpeco1 = stvrtystlpec1.*generuj_maticu;
upravenytretistlpeco1 = tretistlpec1.*generuj_maticu;
upravenydruhystlpeco1 = druhystlpec1.*generuj_maticu;
upravenyprvystlpeco1 = prvystlpec1.*generuj_maticu;
%%pridanie sumu druhy obrazok
upravenyosmystlpeco2 = osmystlpec2.*generuj_maticu;
upravenysiedmystlpeco2 = siedmystlpec2.*generuj_maticu;
upravenysiestystlpeco2 = siestystlpec2.*generuj_maticu;
upravenypiatystlpeco2 = piatystlpec2.*generuj_maticu;
upravenystvrtystlpeco2 = stvrtystlpec2.*generuj_maticu;
upravenytretistlpeco2 = tretistlpec2.*generuj_maticu;
upravenydruhystlpeco2 = druhystlpec2.*generuj_maticu;
upravenyprvystlpeco2 = prvystlpec2.*generuj_maticu;
%%pridanie sumu treti obrazok
upravenyosmystlpeco3 = osmystlpec3.*generuj_maticu;
upravenysiedmystlpeco3 = siedmystlpec3.*generuj_maticu;
upravenysiestystlpeco3 = siestystlpec3.*generuj_maticu;
upravenypiatystlpeco3 = piatystlpec3.*generuj_maticu;
upravenystvrtystlpeco3 = stvrtystlpec3.*generuj_maticu;
upravenytretistlpeco3 = tretistlpec3.*generuj_maticu;
upravenydruhystlpeco3 = druhystlpec3.*generuj_maticu;
upravenyprvystlpeco3 = prvystlpec3.*generuj_maticu;
%%hodnoty obrazkov s pridanym sumom po nasobeni maticou
novyo1=[upravenyprvystlpeco1 upravenydruhystlpeco1 upravenytretistlpeco1 upravenystvrtystlpeco1 upravenypiatystlpeco1 upravenysiestystlpeco1 upravenysiedmystlpeco1 upravenyosmystlpeco1]
novyo2=[upravenyprvystlpeco2 upravenydruhystlpeco2 upravenytretistlpeco2 upravenystvrtystlpeco2 upravenypiatystlpeco2 upravenysiestystlpeco2 upravenysiedmystlpeco2 upravenyosmystlpeco2]
novyo3=[upravenyprvystlpeco3 upravenydruhystlpeco3 upravenytretistlpeco3 upravenystvrtystlpeco3 upravenypiatystlpeco3 upravenysiestystlpeco3 upravenysiedmystlpeco3 upravenyosmystlpeco3]
novyo1msb = [prvystlpec1 druhystlpec1 tretistlpec1 stvrtystlpec1 piatystlpec1 siestystlpec1 siedmystlpec1 upravenyosmystlpeco1]
novyo17b = [prvystlpec1 druhystlpec1 tretistlpec1 stvrtystlpec1 piatystlpec1 siestystlpec1 upravenysiedmystlpeco1 osmystlpec1]
novyo16b = [prvystlpec1 druhystlpec1 tretistlpec1 stvrtystlpec1 piatystlpec1 upravenysiestystlpeco1 siedmystlpec1 osmystlpec1]
novyo15b = [prvystlpec1 druhystlpec1 tretistlpec1 stvrtystlpec1 upravenypiatystlpeco1 siestystlpec1 siedmystlpec1 osmystlpec1]
novyo14b = [prvystlpec1 druhystlpec1 tretistlpec1 upravenystvrtystlpeco1 piatystlpec1 siestystlpec1 siedmystlpec1 osmystlpec1]
novyo13b = [prvystlpec1 druhystlpec1 upravenytretistlpeco1 stvrtystlpec1 piatystlpec1 siestystlpec1 siedmystlpec1 osmystlpec1]
novyo12b = [prvystlpec1 upravenydruhystlpeco1 tretistlpec1 stvrtystlpec1 piatystlpec1 siestystlpec1 siedmystlpec1 osmystlpec1]
novyo1lsb = [upravenyprvystlpeco1 druhystlpec1 tretistlpec1 stvrtystlpec1 piatystlpec1 siestystlpec1 siedmystlpec1 osmystlpec1]

%%%%%
novyo2msb = [prvystlpec2 druhystlpec2 tretistlpec2 stvrtystlpec2 piatystlpec2 siestystlpec2 siedmystlpec2 upravenyosmystlpeco2]
novyo27b = [prvystlpec2 druhystlpec2 tretistlpec2 stvrtystlpec2 piatystlpec2 siestystlpec2 upravenysiedmystlpeco2 osmystlpec2]
novyo26b = [prvystlpec2 druhystlpec2 tretistlpec2 stvrtystlpec2 piatystlpec2 upravenysiestystlpeco2 siedmystlpec2 osmystlpec2]
novyo25b = [prvystlpec2 druhystlpec2 tretistlpec2 stvrtystlpec2 upravenypiatystlpeco2 siestystlpec2 siedmystlpec2 osmystlpec2]
novyo24b = [prvystlpec2 druhystlpec2 tretistlpec2 upravenystvrtystlpeco2 piatystlpec2 siestystlpec2 siedmystlpec2 osmystlpec2]
novyo23b = [prvystlpec2 druhystlpec2 upravenytretistlpeco2 stvrtystlpec2 piatystlpec2 siestystlpec2 siedmystlpec2 osmystlpec2]
novyo22b = [prvystlpec2 upravenydruhystlpeco2 tretistlpec2 stvrtystlpec2 piatystlpec2 siestystlpec2 siedmystlpec2 osmystlpec2]
novyo2lsb = [upravenyprvystlpeco2 druhystlpec2 tretistlpec2 stvrtystlpec2 piatystlpec2 siestystlpec2 siedmystlpec2 osmystlpec2]
%%

novyo3msb = [prvystlpec3 druhystlpec3 tretistlpec3 stvrtystlpec3 piatystlpec3 siestystlpec3 siedmystlpec3 upravenyosmystlpeco3]
novyo37b = [prvystlpec3 druhystlpec3 tretistlpec3 stvrtystlpec3 piatystlpec3 siestystlpec3 upravenysiedmystlpeco3 osmystlpec3]
novyo36b = [prvystlpec3 druhystlpec3 tretistlpec3 stvrtystlpec3 piatystlpec3 upravenysiestystlpeco3 siedmystlpec3 osmystlpec3]
novyo35b = [prvystlpec3 druhystlpec3 tretistlpec3 stvrtystlpec3 upravenypiatystlpeco3 siestystlpec3 siedmystlpec3 osmystlpec3]
novyo34b = [prvystlpec3 druhystlpec3 tretistlpec3 upravenystvrtystlpeco3 piatystlpec3 siestystlpec3 siedmystlpec3 osmystlpec3]
novyo33b = [prvystlpec3 druhystlpec3 upravenytretistlpeco3 stvrtystlpec3 piatystlpec3 siestystlpec3 siedmystlpec3 osmystlpec3]
novyo32b = [prvystlpec3 upravenydruhystlpeco3 tretistlpec3 stvrtystlpec3 piatystlpec3 siestystlpec3 siedmystlpec3 osmystlpec3]
novyo3lsb = [upravenyprvystlpeco3 druhystlpec3 tretistlpec3 stvrtystlpec3 piatystlpec3 siestystlpec3 siedmystlpec3 osmystlpec3]

%%prekodovanie z double na uint, zmena na dec cislo z binarky
novyo1ch = uint8(bi2de(novyo1))
novyo2ch = uint8(bi2de(novyo2))
novyo3ch = uint8(bi2de(novyo3))
novyo1lsbch = uint8(bi2de(novyo1lsb))
novyo1msbch = uint8(bi2de(novyo1msb))
novyo17bch = uint8(bi2de(novyo17b))
novyo16bch = uint8(bi2de(novyo16b))
novyo15bch = uint8(bi2de(novyo15b))
novyo14bch = uint8(bi2de(novyo14b))
novyo13bch = uint8(bi2de(novyo13b))
novyo12bch = uint8(bi2de(novyo12b))

%%%%%
novyo2lsbch = uint8(bi2de(novyo2lsb))
novyo2msbch = uint8(bi2de(novyo2msb))
novyo27bch = uint8(bi2de(novyo27b))
novyo26bch = uint8(bi2de(novyo26b))
novyo25bch = uint8(bi2de(novyo25b))
novyo24bch = uint8(bi2de(novyo24b))
novyo23bch = uint8(bi2de(novyo23b))
novyo22bch = uint8(bi2de(novyo22b))
%%%%

novyo3lsbch = uint8(bi2de(novyo3lsb))
novyo3msbch = uint8(bi2de(novyo3msb))
novyo37bch = uint8(bi2de(novyo37b))
novyo36bch = uint8(bi2de(novyo36b))
novyo35bch = uint8(bi2de(novyo35b))
novyo34bch = uint8(bi2de(novyo34b))
novyo33bch = uint8(bi2de(novyo33b))
novyo32bch = uint8(bi2de(novyo32b))

%%pretvorime matice na 512x512px obrazok
zmeneny1 = reshape(novyo1ch,[512,512])
zmeneny2 = reshape(novyo2ch,[512,512])
zmeneny3 = reshape(novyo3ch,[512,512])
zmeneny1lsb = reshape(novyo1lsbch,[512,512])
zmeneny1msb = reshape(novyo1msbch,[512,512])
zmeneny17b = reshape(novyo17bch,[512,512])
zmeneny16b = reshape(novyo16bch,[512,512])
zmeneny15b = reshape(novyo15bch,[512,512])
zmeneny14b = reshape(novyo14bch,[512,512])
zmeneny13b = reshape(novyo13bch,[512,512])
zmeneny12b = reshape(novyo12bch,[512,512])

%%%%%%%%%
zmeneny2lsb = reshape(novyo2lsbch,[512,512])
zmeneny2msb = reshape(novyo2msbch,[512,512])
zmeneny27b = reshape(novyo27bch,[512,512])
zmeneny26b = reshape(novyo26bch,[512,512])
zmeneny25b = reshape(novyo25bch,[512,512])
zmeneny24b = reshape(novyo24bch,[512,512])
zmeneny23b = reshape(novyo23bch,[512,512])
zmeneny22b = reshape(novyo22bch,[512,512])
%%%%%%
%%%%%%%%%
zmeneny3lsb = reshape(novyo3lsbch,[512,512])
zmeneny3msb = reshape(novyo3msbch,[512,512])
zmeneny37b = reshape(novyo37bch,[512,512])
zmeneny36b = reshape(novyo36bch,[512,512])
zmeneny35b = reshape(novyo35bch,[512,512])
zmeneny34b = reshape(novyo34bch,[512,512])
zmeneny33b = reshape(novyo33bch,[512,512])
zmeneny32b = reshape(novyo32bch,[512,512])
%%%%%%
figure(1);
subplot(3,10,1), imshow(obrazok1), title('Original image 1');
subplot(3,10,11), imshow(obrazok2), title('Original image 2');
subplot(3,10,21), imshow(obrazok3), title('Original image 3');
subplot(3,10,10), imshow(zmeneny1), title('Zmeneny 1');
subplot(3,10,20), imshow(zmeneny2), title('Zmeneny 2');
subplot(3,10,30), imshow(zmeneny3), title('Zmeneny 3');
subplot(3,10,2), imshow(zmeneny1lsb), title('Zmeneny 1 LSB');
subplot(3,10,9), imshow(zmeneny1msb), title('Zmeneny 1 MSB');
subplot(3,10,8), imshow(zmeneny17b), title('Zmeneny 1 7b');
subplot(3,10,7), imshow(zmeneny16b), title('Zmeneny 1 6b');
subplot(3,10,6), imshow(zmeneny15b), title('Zmeneny 1 5b');
subplot(3,10,5), imshow(zmeneny14b), title('Zmeneny 1 4b');
subplot(3,10,4), imshow(zmeneny13b), title('Zmeneny 1 3b');
subplot(3,10,3), imshow(zmeneny12b), title('Zmeneny 1 2b');;

subplot(3,10,12), imshow(zmeneny2lsb), title('Zmeneny 2 LSB');
subplot(3,10,19), imshow(zmeneny2msb), title('Zmeneny 2 MSB');
subplot(3,10,18), imshow(zmeneny27b), title('Zmeneny 2 7b');
subplot(3,10,17), imshow(zmeneny26b), title('Zmeneny 2 6b');
subplot(3,10,16), imshow(zmeneny25b), title('Zmeneny 2 5b');
subplot(3,10,15), imshow(zmeneny24b), title('Zmeneny 2 4b');
subplot(3,10,14), imshow(zmeneny23b), title('Zmeneny 2 3b');
subplot(3,10,13), imshow(zmeneny22b), title('Zmeneny 2 2b');;

subplot(3,10,22), imshow(zmeneny3lsb), title('Zmeneny 3 LSB');
subplot(3,10,29), imshow(zmeneny3msb), title('Zmeneny 3 MSB');
subplot(3,10,28), imshow(zmeneny37b), title('Zmeneny 3 7b');
subplot(3,10,27), imshow(zmeneny36b), title('Zmeneny 3 6b');
subplot(3,10,26), imshow(zmeneny35b), title('Zmeneny 3 5b');
subplot(3,10,25), imshow(zmeneny34b), title('Zmeneny 3 4b');
subplot(3,10,24), imshow(zmeneny33b), title('Zmeneny 3 3b');
subplot(3,10,23), imshow(zmeneny32b), title('Zmeneny 3 2b');;

%%Obrazky 1
obr1 = obrazok1;
zmenenyobr1 = zmeneny1;
[r1, s1] = size(obr1);
N1 = r1*s1;
MSE1 = mean((1/N1)*sum(sum(double(obr1)-double(zmenenyobr1)).^2));
PSNR1 = 10*log10((255^2)/MSE1);
%%Obrazky 2
obr2 = obrazok2;
zmenenyobr2 = zmeneny2;
[r2, s2] = size(obr2);
N2 = r2*s2;
MSE2 = mean((1/N2)*sum(sum(double(obr2)-double(zmenenyobr2)).^2));
PSNR2 = 10*log10((255^2)/MSE2);
%%Obrazky 3
obr3 = obrazok3;
zmenenyobr3 = zmeneny3;
[r3, s3] = size(obr3);
N3 = r3*s3;
MSE3 = mean((1/N3)*sum(sum(double(obr3)-double(zmenenyobr3)).^2));
PSNR3 = 10*log10((255^2)/MSE3);