Denoising of images using principal component analysis and undecimated dual tree complex wavelet transform

Abstract

Here, a method based on the combination of Undecimated Discrete Wavelet Transform (UDWT) and Dual Tree Complex Wavelet Transform (DTCWT) with PCA for denoising images corrupted by Gaussian noise is proposed. The blend of UDWT and DTCWT results in Undecimated Dual Tree Complex Wavelet Transform (UDTCWT) which is a one-to-one relationship between co-located complex coefficients in all sub-bands and offers improved lower scale sub-band localisation together with improved directional selectivity. But each wavelet coefficients and its parent are not aligned properly. The proposed method uses UDTCWT with PCA to obtain the compaction of signal energy in to a few principal components by spreading the noise over all the transformed coefficients. These coefficients allow removing the noise, with a suitable locally adaptive window shrinkage function. This denoising method is tested on standard test images. The results show that this method is better than existing methods in terms of PSNR.