Download Proposal - The University of Texas at Arlington

EE 5359
TOPICS IN SIGNAL PROCESSING
PROJECT PROPOSAL
TWO STAGE IMAGE DENOISING USING LOCAL PIXEL
GROUPING WITH PRINCIPAL COMPONENT
ANALYSIS
Under the guidance of
DR. K. R. RAO
DETARTMENT OF ELECTRICAL ENGINEERING
UNIVERSITY OF TEXAS AT ARLINGTON
Submitted By:
RAMSANJEEV THOTA(1001051651)
[email protected]
List of Acronyms:
CFA
Color filter array
DCT
Discrete cosine transform
DWI
Diffusion weighted images
EKI
Edge keeping index
HARDI
High angular resolution diffusion imaging
LPG
Local pixel grouping
LMSE
Least mean square error
MAD
Minimum absolute difference
MPC
Maximum matching pixel count
NLM
Non local mean
MSE
Mean square error
ODF
Orientation distribution function
PCA
Principal component analysis
PSNR
Peak signal to noise ratio
SSIM
Structural similarity index metric
SSD
Sum of squares differences
SD
Standard deviation
SVD
Singular value decomposition
TVF
Total variation filter
ABSTRACT:
An efficient scheme with principal component analysis (PCA) using local pixel
grouping(LPG) is proposed for denoising images [19]. For a better preservation of image local
structures, a pixel and its nearest neighbors are modeled as a vector variable, whose training
samples are selected from the local window by using block matching based local pixel
grouping(LPG). LPG procedure make sure that only the sample blocks with similar contents are
used in the local statistics calculation for PCA transform estimation, so that the image local
features can be well preserved after coefficient shrinkage in the PCA domain to remove the
noise. The LPG-PCA denoising procedure is iterated one more time to further improve the
denoising performance, and the noise level is adaptively adjusted in the second stage. It will
bepractically proved with examples that the LPG-PCA method achieves very competitive
denoising performance, especially in image structure preservation, compared with other
denoising methods.
OVERVIEW OF LPG - PCA TECHNIQUE:
The proposed method that is ‘Two Stage Image denoising using LPG with PCA’ which is shown
in the figure 1 is a novel approach towards image denoising [19]. PCA is the statistical technique
and depends mostly on the mathematical analysis of the signal such as calculating the
eigenvalues and eigenvectors for the covariance matrix, diagonalizing the matrix . The pixels of
an image are grouped into a vector by using the block matching method, where the LMSE
operator is applied to each and every pixel in the image and compared with that of the central
pixel. Only those pixels which give the result similar to that of the central pixel are considered
and grouped into a vector on which the PCA transformation is applied. Once the image is
transformed using PCA, the inverse PCA transforms will be applied to obtain the denoised
version of the image. The same process is repeated to further denoise the image so as to
remove any noise residual present in the image. The examples of the images which has gone
through all the stages of LPG-PCA algorithm had been displayed in figure 3. MATLAB is the tool
usedin this project to simulate this technique[12].
LPG PCA TECHNIQUE[19]
Figure 1 : LPG-PCA Algorithm
LOCAL PIXEL GROUPING (LPG):
Grouping the training samples similar to the central KxK block in the LxL training window as
shown in the figure2 is indeed a classification problem and thus different grouping methods
such as block matching [19], K-means clustering [21] can be employed.
Block matching will be used in this project as it is simplest and efficient [19].The L x L training
block is selected and various pixels which are to be denoised are grouped into K x K test vectors
from the L x L training vector sample.
Block matching method : [19]
Figure 2 : the way in which pixels are grouped to form a training block and the variable
block in block matching technique
PRINCIPAL COMPONENT ANAYSIS (PCA) :
PCA is a useful statistical technique that has found application in fields such as face recognition
and image compression, and is a common technique for finding patterns in data of high
dimension.
The Algorithm of Principal Component Analysis (PCA) technique: [18]
1. Getting data from the from the block matching technique.
2.Calculate mean for each test vector and subtract the mean from each pixel of that test vector.
3.Calculation of the covariance matrix.
4.Calculation of the eigenvectors and eigenvalues of the covariance matrix.
5. Choosing components and forming a feature vector.
6.Deriving the new data set.
7.Getting the old data back.
Singular value decomposition or Eigen Value decomposition will be used in the project to obtain
the denoised image.
Examples of image denoised by two stage LPG-PCA technique[19]
a)
b)
c)
figure 3: a) original House image
d)
b) noise corrupted House image
after first stage of proposed method
c) Denoised House image
d) Denoised House image after the second stage of
refinement.
Figure 3 shows the examples of the images which are gone through the step by step process of
two stage image denoising by principal component analysis (PCA) with local pixel grouping
(LPG). Figure 3. a. represents the original image of a house without any noise added to it, figure
3. b. represents the image with noise added to it , figure 3. c. represents the image which has
been rectified in stage 1 in the two stage image denoising process and figure 3. d. represents
the final image after two stages of LPG – PCA denoising technique.
Performance Evaluation Metrics:[2],[20]
The PSNR and SSIM are used to evaluate the performance of the method for various images.
PSNR can measure intensity difference between two images but it may fail to describe the
visual perception quality of the image.
SSIM is used for image visual quality assessment.
MSE is defined as [22]
(1.1)
PSNR is defined as [22]
(1.2)
Where x is the original image and y is the distorted image. M and N are the width and height of
an image. L is the dynamic range of the pixel values.
Equation (1.1) defines the mean square error and equation (1.2) defines peak signal to noise
ratio.
If MSE is small enough, it corresponds to a high quality decompressed image.[22]
Structural similarity index metric:[22]
The SSIM is designed to improve on traditional metrics like PSNR and MSE, which have proved
to be inconsistant with human eye perception.[19]
It is a method for measuring the similarity between two images.
SSIM can reflect the structural similarity between the target image and the reference
image.[19]
PROPOSAL
The aim of this proposal is to analyze various types of noises , denoise the noisy image
to the maximum level and obtain acceptable performance. A novel approach of Principal
Component Analysis (PCA) using Local Pixel Grouping (LPG) will be followed to denoise the
images. Structural Similarity index metric (SSIM) [2] and Peak Signal to Noise Ratio (PSNR), [18]
are the metrics considered to evaluate the performance of this method. Various performance
evaluation metrics such as Mean Square Error, Peak Signal to Noise Ratio, Signal to Noise Ratio,
Structural Similarity Index and Edge Keeping Index (EKI)[19],[20] will be used. The main aim of
the proposed method is to obtain better values for the SSIM and PSNR metrics.
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