Introduction
description
Transcript of Introduction
Seminar on “ Image Denoising Method based on Curvelet Transform” Master of Engineering (Electronics and Communication ) Year 2011-12.
Rajput Sandeep Kumar Jawaharlal (100370704036)
Prepared By: Guided By: Rajput Sandeep J Prof. A.R. Yadav ME (EC-213) Professor , EC Dept. PIET, Limda. PIET, Limda.
Introduction Image acquired through sensors charge coupled device (CCD)
cameras may be influenced by noise sources.
Image processing technique also corrupts image with noise, leading to significant reduction in quality.
Traditionally, Linear filters Edge preserving smoothing algorithm
New Methods, Non-linear techniques : Wavelet Transform : Curvelet Transform
Original Image
Sub-band decomposition
Smooth partitioning andRenormalization
Each subzone of each block to carry out analysis of the Ridgelet
Block image n x n
Ridgelet Transform
Radon Transform
WT 1D
Ang
le
Inverse FFT 1 D
FFT 2D
Frequency
WT 2D
Process of Curvelet Transform
Figure: 1 Curvelet transform flow block diagram
Sub-band Decomposition
fP0 f1 f2
f ,,, 210 fffPf
Smooth Partitioning
Smooth Partitioning The windowing function w is a nonnegative smooth
function. Partition of the intensity:
The intensity of certain pixel (x1,x2) is divided between all sampling windows of the grid.
1,21 ,
22112
kk
kxkxw
Ridgelet are an orthonormal set {} for L2(R2).
Ridgelet Analysis
2-s
2-2s
1
2-s
2s
radius 2s
2s
divisions
Ridge in Square It’s Fourier TransformRidge in Square
Ridgelet TilingFourier Transform
within Tiling
Ridgelet Analysis
The ridgelet element in the frequency domain:
where, i,l are periodic wavelets for [-, ).i is the angular scale.j,k are wavelets for R.j is the ridgelet scale and k is the ridgelet location.
πθωψθωψρ likjlikjλ ,,,,2
1 ξˆξˆξξˆ 21
Curvelet TransformThe four stages of the Curvelet Transform were: Sub-band decomposition
Smooth partitioning
Renormalization
Ridgelet analysis
,,, 210 fffPf
fwh sQQ
QQQ hTg 1
λQQ,λ ρgα ,
Image ReconstructionThe Inverse of the Curvelet Transform: Ridgelet Synthesis
Renormalization
Smooth Integration
Sub-band Recomposition
λλ
Q,λQ ραg
QQQ gTh
sQ
QQs hwfQ
s
ss ffPPf 00
Thresholding methodsWindow Shrink Method
Set di, j is the parameter which is from curvelet transformed noise image; choose a di, j centered window of n×n as the processing subject.
3X 3 Window Shrink
The curvelet coefficients to be thresholded
Set Symbolic function:
σ is the variance of Gaussian white noise in the image , then
shrinking processing parameter is
Then the thresholded parameter can be calculated as:
Thresholding methodsThe sum of all the parameter’s square in the n×n window is
calculated.
Bayes Shrink method
Thresholding methods
In this method σ2D is the variance of an image containing
noise, σ2 is the variance of noise, and σ2X is the original
image’s variance.Now, noise variance is:
The variance of original image is calculated by, Setting Threshold is σ2 / σ2
X then begin the processing of removing noise.
Combination of Window shrink and Bayes shrink
The variance σ2X is estimated of the original picture using Bayes
shrink theory, then η is calculated using σ2X instead of the noise
variance σ 2,such as
At last shrink factors αi, j are known and the noise coefficient is filtered out by taking advantage of αi, j.
Thresholding methods
x
Thresholding methods
Image denoising Algorithm
Original image σ = 20 noise image
2-D Wavelet transform Traditional Curvelet transform
Image denoising Algorithm
Quad tree Decomposition algorithm
Now, The Q(x,y) that define the matrix of mxm image and S(vi) denote the element of the Q(x,y) where vi denote the number of decomposition required for that element.
Image denoising Algorithm Algorithm : Denote result image of improved algorithm as R, this pixel
fusion based algorithm is described as follows. Applying wavelet transform to obtain result image W. Applying curvelet transform to obtain result image C. Get quad tree matrix Q with applying quad tree
decomposition to C. R(x, y) is calculated as R(x, y) = cW(x, y) + dC(x, y) Where,
Image denoising Algorithm
Result of algorithm
Original image σ = 20 noise image Improved Curvelet transform
Image denoising Algorithm
Image denoising Algorithm
Conclusion To overcome the disadvantages of the wavelet
transform along the curves in the images the curvelet transform is used and it gives high PSNR.
A new method of combination of the Window Shrink and Bayes Shrink based on Curvelet transform is used to remove noise from image. It has better PSNR. So the image we get by this method is better and that of the traditional wavelet methods.
Referencesi. Introduction to Wavelet: Bhushan D Patil PhD Research Scholar Department of Electrical Engineering Indian Institute
of Technology, Bombay.
ii. Pixel Fusion Based Curvelets and Wavelets Denoise Algorithm, Liyong Ma, Member, IAENG, Jiachen Ma and Yi Shen Advance online publication: 16 May 2007
iii. The Curvelet Transform - Jean-Luc Starck, Emmanuel J. Candès, and David L. Donoho IEEE transactions on image processing, vol. 11, no. 6, june 2002.
iv. Image denoising using wavelet transform: an approach for edge Preservation Received 03 March 2009; revised 24 November 2009; accepted 25 November 2009
v. Image Denoising Method Based on Curvelet Transform -University of Science and Technology, IEEE transactions on image processing, vol. 11, no. 6, june 2008.
vi. New Method Based on Curvelet Transform for Image Denoising Donglei Li, Zhemin Duan, Meng Jia
vii. Department of Electronics and Information Northwestern Polytechnical University, China, 2010 International Conference on Measuring Technology and Mechatronics Automation
viii. Improved Image Denoising Method based on Curvelet Transform Proceedings of the 2010 IEEE International Conference on Information and Automation June 20 - 23, Harbin, China
ix. Image Denoising Based on Curvelet Transform and Continuous Threshold YUAN Ruihong TANG Liwei WANG Ping YAO Jiajun Department of Artillery Engineering Ordnance Engineering College Shijiazhuang ,China, 2010 First International Conference on Pervasive Computing, Signal Processing and Applications.
Thank You