Common spatial patterns (CSP) is a commonly used method of spatial filtering for multichannel electroencephalogram (EEG) signals. The formulation of the CSP criterion is based on variance using L2-norm, which implies that CSP is sensitive to outliers. In this paper, we propose a robust version of CSP, called CSP-L1, by maximizing the ratio of filtered dispersion of one class to the other class, both of which are formulated by using L1-norm rather than L2-norm. The spatial filters of CSP-L1 are obtained by introducing an iterative algorithm, which is easy to implement and is theoretically justified. CSP-L1 is robust to outliers. Experiment results on a toy example and datasets of BCI competitions demonstrate the efficacy of the proposed method.

In this paper, we propose a novel optimal spatio-temporal filter, termed local temporal common spatial patterns (LTCSP), for robust single-trial elctroencephalogram (EEG) classification. Different from classical common spatial patterns (CSP) that uses only global spatial covariances to compute the optimal filter, LTCSP considers temporally local information in the variance modelling. The underlying manifold variances of EEG signals contain more discriminative information. LTCSP is an extension to CSP in the sense that CSP can be derived from LTCSP under a special case. By constructing an adjacency matrix, LTCSP is formulated as an eigenvalue problem. So, LTCSP is computationally as straightforward as CSP. However, LTCSP has better discrimination ability than CSP and is much more robust. Simulated experiment and real EEG classification demonstrate the effectiveness of the proposed LTCSP method.

Dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning. Linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze. In this paper, we propose an essentially linear projection technique, called locality-preserved maximum information projection (LPMIP), to identify the underlying manifold structure of a data set. LPMIP considers both the within-locality and the between-locality in the processing of manifold learning. Equivalently, the goal of LPMIP is to preserve the local structure while maximize the out-of-locality (global) information of the samples simultaneously. Different from principal component analysis (PCA) that aims to preserve the global information and locality-preserving projections (LPPs) that is in favor of preserving the local structure of the data set, LPMIP seeks a tradeoff between the global and local structures, which is adjusted by a parameter alpha, so as to find a sub- space that detects the intrinsic manifold structure for classification tasks. Computationally, by constructing the adjacency matrix, LPMIP is formulated as an eigenvalue problem. LPMIP yields orthogonal basis functions, and completely avoids the singularity problem as it exists in LPP. Further, we develop an efficient and stable LPMIP/QR algorithm for implementing LPMIP, especially, on high-dimensional data set. Theoretical analysis shows that conventional linear projection methods such as (weighted) PCA, maximum margin criterion (MMC), linear discriminant analysis (LDA), and LPP could be derived from the LPMIP framework by setting different graph models and constraints. Extensive experiments on face, digit, and facial expression recognition show the effectiveness of the proposed LPMIP method.

In this letter, we present an efficient algorithm for the removal of random-valued impulse noise from a corrupted image by using a reference image. The proposed method uses a statistic of rank-ordered relative differences to identify pixels which are likely to be corrupted by impulse noise. Once a noisy pixel is identified, its value is restored by a simple weighted mean filter. Simulation results indicate that our algorithm provides a significant improvement over many other existing techniques.