This Presentation includes how to denoise image using Matlab.

1. A MINOR PROJECT PRESENTATION PREPARED BY-NIKHIL
KUMAR-0511EC111056
AMAN PRAKASH-0511EC111007
Guided By –
Prof. Rajesh Kumar Rai

2. CONTENTS….
• Introduction.
• Fourier analysis.
• Wavelet analysis.
• Wavelet analysis cont.…..
• Algorithm for image denoising.
• Illustrations.
Software Detail
 MATLAB R2012a
 Version (7.14.0.739)
 64 Bit
 License no.-161052

3. INTRODUCTION
• Image denoising refers to the recovery of a digital image that has been
contaminated by additive white Gaussian noise (AWGN).
• Wavelet transform enable us to represent signals with a high degree of
scarcity. This is the principle behind a non-linear wavelet based signal
estimation technique known as wavelet denoising.
• Curved wavelet transform is a new multi-scale representation most
suitable for objects with curves.
• It developed by candès and donoho in 1999. This technique is Still not
fully matured but seems promising however.

4. FOURIER
ANALYSIS
• Breaks down a signal into constituent
sinusoids of different frequencies. In
other words: transform the view of the
signal from time-base to frequency-base.
• By using Fourier transform , we loose
the time information : when did a
particular event take place. FT can not
locate drift, trends, abrupt changes,
beginning and ends of events, etc.
Calculating use complex numbers.

5. WAVELET
ANALYSIS
• A wavelet is a waveform of effectively
limited duration that has an average
value of zero.
• The DWT is identical to a hierarchical
sub band system. In DWT ,the original
image is transformed into different level
say four pieces which is normally
labelled as A1,H1,V1 and D1.The A1
sub-band called the approximation, can
be further decomposed into four sub-bands.
The remaining bands are called
detailed components.

6. WAVELET ANALYSIS CONT.…..
• The image de-noising is the process to remove the noise from the image naturally corrupted by the noise.
The wavelet method is one among. The wavelet techniques are very effective to remove the noise because
of its ability to capture the energy of a signal in few energy Transform values. The wavelet methods are
based on shrinking the wavelet Coefficients in the wavelet domain. The objective is to remove the noise
without affecting the important feature of the image. The most commonly used procedure to remove the
noise is wavelet shrinkage by non-linear method proposed by donoho and Johnston (1994, 1995). In
Statistical context this can be referred as the estimation of the true curve from the Data contaminated with
the noise usually assume to be Gaussian noise. The estimation of the true curve involves three steps.
• Apply DWT which transforms the discrete data from time domain into time-frequency Domain. The
values of the transformed data in time-frequency domain are called the coefficients. The coefficients
with small absolute values dominated by noise, While the coefficients with large absolute values carry
more data information than Noise.
• In the second step the wavelet coefficient are set to zero (hard threshold Rule) or shrink (soft threshold
rule), if they are not crossing certain threshold Level.
• The last step is to reconstruct the signal from the resultant coefficient using IDWT.

7. • The simplest example of wavelet basis is haar basis (haar, 1910) which uses scaling function and
mother wavelet given by.
• In case of two dimension, the scaling function and the wavelets are defined as follows
where s = h; v; d are horizontal, vertical and diagonal details respectively defined
as

8. ALGORITHM FOR DENOISING
• Open Matlab and in command window type the function wavemenu.
• Select wavelet 2-D from the wavelet toolbox menu.
• Load the image in the wavelet 2-D window.
• Select Haar wavelet and set the decomposition level to 5 and analyse the image.
• Compress the image using level thresholding by thresholding at Scare high.
• Then denoised the image by Penalizing the image at high threshold level.

9. • Wavemenu : Wavemenu opens a menu for accessing the various graphical tools provided in the
Wavelet Toolbox™ software.
• Wavelet 2-D: Wavelet Toolbox™ provides wavelet 2-D functions and an app for developing
wavelet-based algorithms for the analysis, synthesis, denoising, and compression of signals and
images.
• Haar wavelet: The Haar transform is the simplest orthogonal wavelet transform. It is computed
by iterating difference and averaging between odd and even samples of the signal.
• Decomposition level: Iterating the decomposition process, breaks the input signal into many
lower-resolution components: Wavelet decomposition tree or Square wavelet Decomposition.
• Thresholding: Image thresholding is a simple, yet effective, way of partitioning an image into a
foreground and background. Image thresholding is most effective in images with high levels of
contrast. Common image thresholding algorithms include histogram and multi-level thresholding.
• Thresholding at Scare high: This is basically a level of thresholding to compress the image and
for smoothening of image.
• Penalizing: Threshold is obtained by a wavelet packet coefficients selection rule using a
penalization method provided by Birge-Massart.

11. ILLUSTRATIONS…..
AIM

19. Denoised Image

20. THANKS