Under the guidance of Dr. K R. Rao Ramsanjeev Thota( )

List of Acronyms: List of Acronyms: CFAColor filter array DCTDiscrete cosine transform DWIDiffusion weighted images EKI Edge keeping index HARDI High angular resolution diffusion imaging LPGLocal pixel grouping LMSELeast mean square error MADMinimum absolute difference MPCMaximum matching pixel count NLMNon local mean MSEMean square error ODF Orientation distribution function PCA Principal component analysis PSNRPeak signal to noise ratio SSIMStructural similarity index metric SSDSum of squares differences SDStandard deviation SVDSingular value decomposition TVFTotal variation filter

INTRODUCTION Images are corrupted by noise during transmission and acquisition Various linear and non linear models have been proposed in order to get rid of noise but have their own drawbacks. Principal component analysis (PCA) is a popular method that has yielded good results in image de- noising.

OBJECTIVE The project aims to denoise the noisy image to the maximum level and obtain acceptable performance. A study will be done on types of noises, various performance evaluation tools and the key techniques Local Pixel Grouping and Principal Component Analysis Peak Signal to Noise Ratio(PSNR) and Structural Similarity Index(SSIM) are used as evaluation metrics.

LPG PCA Transforma tion Inverse PCA Transforma tion Inverse PCA Transformat ion PCA Transformat ion LPG 1 st Stage 2 nd Stage Denoised Image Denoised Image After 1 st stage FIGURE 1: LPG – PCA based Algorithm METHODOLOGY [5]

LOCAL PIXEL GROUPING Different grouping techniques such as block matching [19], k-means clustering [21] can be employed. Block matching is used in this project for LPG. Grouping the training samples similar to the central KxK block in the LxL training window. FIGURE 2: Figure 2 shows the way in which pixels are grouped to form a training block and the variable block in block matching technique. ]

PRINCIPAL COMPONENT ANALYSIS PCA is a classical decorrelation technique in statistical signal processing. [18],[19] By transforming the original dataset into PCA domain and preserving only the several most significant principal components, the noise and trivial information can be removed.[19] Advantage of PCA is that you compress the data without much loss of information. [18]

Steps for PCA [18] Getting data Mean calculation and mean subtraction from each pixel Calculation of covariance matrix Calculation of eigenvectors and eigenvalues of covariance matrix Deriving the new data set Getting the old data back

EXAMPLE [19] a) original House image b) noise corrupted House image a) b)

c) Denoised House image after first stage of LPG-PCA method d) Denoised House image after the second stage of LPG-PCA method. c) d)

APPLICATIONS OF PCA[1],[4],[18] Used for Image compression Used for finding patterns Used in Image representation A clear study on applications of PCA will be done in the project.

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