Denoising and Dimensionality Reduction of Hyperspectral Images Using Framelet Transform with Different Shrinkage Functions

Abstract

Present study is focussed on providing alternatives beyond discrete wavelet transform that not only reduce the dimensionality of the data and also simultaneously denoised the data cube by combining framelet transform (FRT) with different shrinkage functions and dimensionality reduction methods. Universal shrink (US), Visu shrink (VS), Minimax shrink (MS), Sure shrink (SS), Bayes shrink (BS) and Normal shrink (NS) will be applied to threshold the detail coefficients of framelet transform. Discrete wavelet transform (DWT), wavelet packet transform (WPT) and curvelet transform (CUT) also used for evaluating the performance of the proposed method. Peak signal to noise ratio (PSNR) is calculated for each method and the results are compared. A higher value of the PSNR indicates the good quality of the denoised data cube. Then dimensionality reduction methods such as principal component analysis (PCA), Singular value decomposition (SVD) and Linear discriminant analysis (LDA) are applied on the denoised data cube. The efficiency of the simultaneous denoising and dimensionality reduction of hyperspectral data cube is calculated in terms of entropy with and without denoising. Edge detection also performed, directional properties of framelet transform can able to capture edges and contours which are the main features in images. The framelet transform, Bayes shrink with soft thresholding produce sound results in terms of denoising and edge detection over DWT, WPT and curvelet transform based methods.