Kernel principal component analysis (KPCA) for the de-noising of communication signals

This paper is concerned with the problem of de-noising for non-linear signals. Principal Component Analysis (PCA) cannot be applied to non-linear signals however it is known that using kernel functions, a non-linear signal can be transformed into a linear signal in a higher dimensional space. In that feature space, a linear algorithm can be applied to a non-linear problem. It is proposed that using the principal components extracted from this feature space, the signal can be de-noised in its input space

Statistical Shape Analysis using Kernel PCA

©2006 SPIE--The International Society for Optical Engineering. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. The electronic version of this article is the complete one and can be found online at: http://dx.doi.org/10.1117/12.641417DOI:10.1117/12.641417Presented at Image Processing Algorithms and Systems, Neural Networks, and Machine Learning, 16-18 January 2006, San Jose, California, USA.Mercer kernels are used for a wide range of image and signal processing tasks like de-noising, clustering, discriminant analysis etc. These algorithms construct their solutions in terms of the expansions in a high-dimensional feature space F. However, many applications like kernel PCA (principal component analysis) can be used more effectively if a pre-image of the projection in the feature space is available. In this paper, we propose a novel method to reconstruct a unique approximate pre-image of a feature vector and apply it for statistical shape analysis. We provide some experimental results to demonstrate the advantages of kernel PCA over linear PCA for shape learning, which include, but are not limited to, ability to learn and distinguish multiple geometries of shapes and robustness to occlusions

On pre-image iterations for speech enhancement

In this paper, we apply kernel PCA for speech enhancement and derive pre-image iterations for speech enhancement. Both methods make use of a Gaussian kernel. The kernel variance serves as tuning parameter that has to be adapted according to the SNR and the desired degree of de-noising. We develop a method to derive a suitable value for the kernel variance from a noise estimate to adapt pre-image iterations to arbitrary SNRs. In experiments, we compare the performance of kernel PCA and pre-image iterations in terms of objective speech quality measures and automatic speech recognition. The speech data is corrupted by white and colored noise at 0, 5, 10, and 15 dB SNR. As a benchmark, we provide results of the generalized subspace method, of spectral subtraction, and of the minimum mean-square error log-spectral amplitude estimator. In terms of the scores of the PEASS (Perceptual Evaluation Methods for Audio Source Separation) toolbox, the proposed methods achieve a similar performance as the reference methods. The speech recognition experiments show that the utterances processed by pre-image iterations achieve a consistently better word recognition accuracy than the unprocessed noisy utterances and than the utterances processed by the generalized subspace method

Enhancing Hyperspectral Image Quality using Nonlinear PCA

International audienceIn this paper, we propose a new method aiming at reducing the noise in hyperspectral images. It is based on the nonlinear generalization of Principal Component Analysis (NLPCA). The NLPCA is performed by an auto associative neural network that have the hyperspectral image as input and is trained to reconstruct the same image at the output. Thanks to its bottleneck structure, the AANN forces the hyper spectral image to be projected in a lower dimensionality feature space where noise as well as both linear and nonlinear correlations between spectral bands are removed. This process permits to obtain enhancements in terms of hyperspectral image quality. Experiments are conducted on different real hyper spectral images, with different contexts and resolutions. The results are qualitatively and quantitatively discussed and demonstrate the interest of the proposed method as compared to traditional approaches