A LULU noise removal algorithm for images using principal component analysis

Abstract

There are various methods to efficiently denoise an image, one method is Principle Component Analysis (PCA). Classical PCA reduces the dimensionality of a dataset, transforming the original dataset to preserve only significant principle components hence removing noise and trivial information from the image. The implementation of˘a PCA with local pixel grouping (LPG) in statistical signal processing, ensures that an image’s local features are effectively preserved and the noise removed. The LPG-PCA based denoising scheme investigated in Zhang et al. (Zhang, Dong, Zhang and Shi, 2010) is spatially adaptive and used a local window combined with LPG to extract similar training samples for PCA estimation. We propose using the LULU smoother with Zhang et al.’s LPG-PCA algorithm to remove noise from images corrupted with Gaussian, Gumbel and speckle noise. Our proposed LULU LPG-PCA algorithm is an improvement of Zhang et al.’s LPG-PCA algorithm. Since the resultant images and quality performance measure, the structural similarity index (SSIM) values obtained for the proposed LULU LPG-PCA algorithm were superior in comparison to Zhang et al.’s LPG-PCA algorithm for different noise types and varying noise levels. The results obtained highlight the versatile ability of the LULU smoother to tackle different noise types and noise levels when combined with Zhang et al.’s LPG-PCA algorithm. Our proposed LULU LPG-PCA algorithm achieves a very competitive denoising performance in comparison to Zhang et al.'s established LPG-PCA algorithm and in some cases outperforms it for different noise types when the noise corruption is more extensive, which is associated with greater noise levels.