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 methods

Window 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.