This document discusses noise estimation and filtering in images. It defines different types of image noise including Gaussian noise, salt and pepper noise, and speckle noise. For each noise type, it describes the cause and appearance. It then explains techniques for filtering each noise type, such as using median filters for salt and pepper noise and mean filters for speckle noise. Finally, it discusses applications of image denoising in areas like medical imaging and image processing.

1. Noise Estimation and
Filtering
Submitted By:
Poulomi Dutta - C91/MCA/212018
Sucheta Goswami- C91/MCA/212027
Sudip Kumar Ghosh- C91/MCA/212028

2. INTRODUCTION
What is Noise in Image ?
 Image noise is random variation of brightness or color information in
images, and is usually an aspect of electronic noise.
 It can be produced by the image sensor and circuitry of a scanner or
digital camera.
 It is a degradation, in a image signal, caused by external disturbances.
 Noise is caused due to various sources which include many
environmental factors which includes noise like Gaussian, Poisson ,
Blurred , Speckle and salt-and-pepper noise.

3. Types of Image Noise
Gaussian Noise
Salt and Pepper Noise
Speckle Noise

4. 1.Gaussian Noise
 It is statistical noise having a probability distribution function(PDF)
equal to that of the normal distribution.
 The probability density function of a Gaussian random variable is
given by
Where z : grey level
μ : mean grey value
: standard deviation.
 Also called as additive noise as each pixel is modified such that a
certain distribution is added to each pixel.
 Caused due to poor illumination during capture or due to high
temperatures and can also be caused due to noise present in
electronic circuits.
 The specified range of variance is 0.0-65025.0 (The higher the
values in the range, the noisier the image will be.) and of mean is
0.0-255.0 (The higher the mean value, the brighter the image will
be.)
Mean = 100
Variance limit = [1000, 10000]
Mean = 0
Variance limit = [65025, 65025]
Mean = 240 (out of 255)
Variance limit = [0, 0]
The original image:
Mean = 0
Variance limit = [0, 0]

5. Gaussian Blur
•In digital image processing Gaussian noise can be reduced using a spatial filter.
•Conventional spatial filtering techniques for noise removal include: mean (convolution)
filtering, median filtering and Gaussian smoothing.
Gaussian Smoothing (Gaussian Blur):
•A Gaussian blur is applied by convolving the image with a Gaussian function.
•The values from this function will create the convolution matrix / kernel that will be applied to every
pixel in the original image. This convolution creates a normal distribution of those pixel values,
smoothing out some of the randomness.
In this case,4 x 200 + 2 x (200 + 200 + 100 + 100) + 1
x (200 + 200 + 200 + 100) = 2700.
We divide this by 16 (the sum of 4, 2 x 4 and 1 x 4)
to get 168.75. The colour will be in between blue
and pink but more to the pink side.
By multiplying the grid we get 900. Then,
we divide this by the number of pixels, that
is 4. So 900 / (4 + 2 + 2 + 1) = 100, this one
stayes the same.
x and y specify the distance of horizontal and vertical axis
from the centre pixel (0,0).
A halftone print rendered smooth
through Gaussian blur
start by placing the filter

6. 2. Salt and Pepper Noise
 Also referred to as Impulse Noise.
 In this type of noise, the images would get the dark pixels in the bright
regions and the bright pixels in the dark regions.
 This noise is generally caused by sudden disturbances during capturing of
the image, also errors in data transmission, failure in memory cell or analog-
to-digital converter errors.
 As an impact ,the image would have lot of white(salt) and black(pepper)
spots.
 Salt value is in grey level- 255 (brightest) and pepper value is in grey level- 0
(darkest),so
10 10 251
10 10 251
10 10 10
253 253 10
253 253 253
253 10 253
Salt Noise Pepper Noise

7. Filtering techniques to remove noises in the image?
Some of the filters we can use to remove salt noise or
pepper noise are:
 Max filter : This filter is useful for finding the brightest
points in an image.We can remove pepper noise by
using max filter.
 Min filter : This filter is useful for finding the darkest
points in an image. We can remove salt noise by using
min filter.
Median filter : Process is replaces the value of a pixel
by the median of the gray levels in region Axy of that
pixel. We can remove salt and pepper noise by using
median filter.

8. MEDIAN FILTER
 Median filtering is excellent at reducing Salt and Pepper noise. The filtering algorithm will scan the
entire image, using a small matrix, and recalculate the value by sorting the set of pixels and take
the center pixel values inside the matrix.
 The median m of a set of values is such that half of the values are greater than m and half are less
than m.
 With the example above, the sorted values are,
 Median of this set is 34.
 Example for Median filtering,
(a)Corrupted image with salt and pepper noise, (b)Noise reduction in 3X3 averaging filter , (c) Noise reduction in 3X3 median Filter.

9. 3. Speckle Noise
• Speckle noise is a multiplicative noise that affects pixels in a gray-scale image, and
mainly occurs in low level luminance images.
• In Speckle noise pixel value is multiplied by a random value.
• The distribution noise can be expressed as –
• Where G(x, y) is the observed image, F(x, y) is the input image and U(x, y) is the multiplicative component of
the speckle noise.
• It increases the mean gray level of a local area.
G(x, y) = F(x, y) * U(x, y)

10. MEAN / AVERAGE FILTER
• Mean (average) filter is the simplest linear filter.
• Replace each pixel value in an image with the mean value of its neighbors,
including itself.
• Advantage :
 Easy to implement
 Used to remove the Speckle noise
• Disadvantage :
 It does not preserve details of image. Some details are removes of image with using the
mean filter.
 Example :

11. TYPES OF NOISES (CODE) :

12. TYPES OF FILTERING (CODE) :

13. Applications:-
• In medical imaging application for the
study of anatomical structure and image
processing of MRI medical images.
• Image denoising plays an important role in a wide range of applications such as
image restoration,
 visual tracking,
image registration,
image segmentation, and
 image classification,
where obtaining the original image content is crucial for strong performance.