Divergence Framework for EEG based Multiclass Motor Imagery Brain Computer Interface

Similar to most of the real world data, the ubiquitous presence of non-stationarities in the EEG signals significantly perturb the feature distribution thus deteriorating the performance of Brain Computer Interface. In this letter, a novel method is proposed based on Joint Approximate Diagonalization (JAD) to optimize stationarity for multiclass motor imagery Brain Computer Interface (BCI) in an information theoretic framework. Specifically, in the proposed method, we estimate the subspace which optimizes the discriminability between the classes and simultaneously preserve stationarity within the motor imagery classes. We determine the subspace for the proposed approach through optimization using gradient descent on an orthogonal manifold. The performance of the proposed stationarity enforcing algorithm is compared to that of baseline One-Versus-Rest (OVR)-CSP and JAD on publicly available BCI competition IV dataset IIa. Results show that an improvement in average classification accuracies across the subjects over the baseline algorithms and thus essence of alleviating within session non-stationarities

Multiclass Common Spatial Pattern for EEG based Brain Computer Interface with Adaptive Learning Classifier

In Brain Computer Interface (BCI), data generated from Electroencephalogram (EEG) is non-stationary with low signal to noise ratio and contaminated with artifacts. Common Spatial Pattern (CSP) algorithm has been proved to be effective in BCI for extracting features in motor imagery tasks, but it is prone to overfitting. Many algorithms have been devised to regularize CSP for two class problem, however they have not been effective when applied to multiclass CSP. Outliers present in data affect extracted CSP features and reduces performance of the system. In addition to this non-stationarity present in the features extracted from the CSP present a challenge in classification. We propose a method to identify and remove artifact present in the data during pre-processing stage, this helps in calculating eigenvectors which in turn generates better CSP features. To handle the non-stationarity, Self-Regulated Interval Type-2 Neuro-Fuzzy Inference System (SRIT2NFIS) was proposed in the literature for two class EEG classification problem. This paper extends the SRIT2NFIS to multiclass using Joint Approximate Diagonalization (JAD). The results on standard data set from BCI competition IV shows significant increase in the accuracies from the current state of the art methods for multiclass classification

Joint Approximate Covariance Diagonalization with Applications in MIMO Virtual Beam Design

We study the problem of maximum-likelihood (ML) estimation of an approximate common eigenstructure, i.e. an approximate common eigenvectors set (CES), for an ensemble of covariance matrices given a collection of their associated i.i.d vector realizations. This problem has a direct application in multi-user MIMO communications, where the base station (BS) has access to instantaneous user channel vectors through pilot transmission and attempts to perform joint multi-user Downlink (DL) precoding. It is widely accepted that an efficient implementation of this task hinges upon an appropriate design of a set of common "virtual beams", that captures the common eigenstructure among the user channel covariances. In this paper, we propose a novel method for obtaining this common eigenstructure by casting it as an ML estimation problem. We prove that in the special case where the covariances are jointly diagonalizable, the global optimal solution of the proposed ML problem coincides with the common eigenstructure. Then we propose a projected gradient descent (PGD) method to solve the ML optimization problem over the manifold of unitary matrices and prove its convergence to a stationary point. Through exhaustive simulations, we illustrate that in the case of jointly diagonalizable covariances, our proposed method converges to the exact CES. Also, in the general case where the covariances are not jointly diagonalizable, it yields a solution that approximately diagonalizes all covariances. Besides, the empirical results show that our proposed method outperforms the well-known joint approximate diagonalization of eigenmatrices (JADE) method in the literature.Comment: 6 pages, 3 figure

Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images

Optical Coherence Tomography (OCT) is an emerging technique in the field of biomedical imaging, with applications in ophthalmology, dermatology, coronary imaging etc. OCT images usually suffer from a granular pattern, called speckle noise, which restricts the process of interpretation. Therefore the need for speckle noise reduction techniques is of high importance. To the best of our knowledge, use of Independent Component Analysis (ICA) techniques has never been explored for speckle reduction of OCT images. Here, a comparative study of several ICA techniques (InfoMax, JADE, FastICA and SOBI) is provided for noise reduction of retinal OCT images. Having multiple B-scans of the same location, the eye movements are compensated using a rigid registration technique. Then, different ICA techniques are applied to the aggregated set of B-scans for extracting the noise-free image. Signal-to-Noise-Ratio (SNR), Contrast-to-Noise-Ratio (CNR) and Equivalent-Number-of-Looks (ENL), as well as analysis on the computational complexity of the methods, are considered as metrics for comparison. The results show that use of ICA can be beneficial, especially in case of having fewer number of B-scans

Generalized Non-orthogonal Joint Diagonalization with LU Decomposition and Successive Rotations

Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset, and thus is insufficient to handle multiple datasets with inter-set dependences, a scenario often encountered in joint BSS (J-BSS) applications. As such, we present a generalized NJD (GNJD) algorithm to simultaneously perform asymmetric NJD upon multiple sets of target matrices with mutually linked loading matrices, by using LU decomposition and successive rotations, to enable J-BSS over multiple datasets with indication/exploitation of their mutual dependences. Experiments with synthetic and real-world datasets are provided to illustrate the performance of the proposed algorithm.Comment: Signal Processing, IEEE Transactions on (Volume:63 , Issue: 5

Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions a joint diagonalizer is unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in a closed form in terms of an eigenvalue and a singular value decomposition of two matrices.Comment: 23 page

On Channel Inseparability and the DoF Region of MIMO Multi-way Relay Channels

Full-duplex multi-way relaying is a potential solution for supporting high data rates in future Internet-of-Things (IoT) and 5G networks. Thus, in this paper the full-duplex MIMO multi-way channel consisting of 3 users (Y-channel) with $M$ antennas each and a common relay node with $N$ antennas is studied. Each user wants to exchange messages with all the other users via the relay. A transmission strategy is proposed based on channel diagonalization that decomposes the channel into parallel sub-channels, and physical-layer network coding over these sub-channels. It is shown that the proposed strategy achieves the optimal DoF region of the channel if $N\leq M$. Furthermore, the proposed strategy that requires joint encoding over multiple sub-channels is compared to another strategy that encodes over each sub-channel separately. It turns out that coding jointly over sub-channels is necessary for an optimal transmission strategy. This shows that the MIMO Y-channel is inseparable.Comment: to appear in the ITG Conference on Systems, Communications and Coding (SCC), 201

Three approaches for representing Lindblad dynamics by a matrix-vector notation

Markovian dynamics of open quantum systems are described by the L-GKS equation, known also as the Lindblad equation. The equation is expressed by means of left and right matrix multiplications. This formulation hampers numerical implementations. Representing the dynamics by a matrix-vector notation overcomes this problem. We review three approaches to obtain such a representation. The methods are demonstrated for a driven two-level system subject to spontaneous emission.Comment: 17 page

Simultaneous Diagonalization: On the DoF Region of the K-user MIMO Multi-way Relay Channel

The K-user MIMO Y-channel consisting of K users which want to exchange messages among each other via a common relay node is studied in this paper. A transmission strategy based on channel diagonalization using zero-forcing beam-forming is proposed. This strategy is then combined with signal-space alignment for network-coding, and the achievable degrees-of-freedom region is derived. A new degrees-of-freedom outer bound is also derived and it is shown that the proposed strategy achieves this outer bound if the users have more antennas than the relay.Comment: 6 pages, accepted for publication in EW 201

Blind Source Separation: Fundamentals and Recent Advances (A Tutorial Overview Presented at SBrT-2001)

Blind source separation (BSS), i.e., the decoupling of unknown signals that have been mixed in an unknown way, has been a topic of great interest in the signal processing community for the last decade, covering a wide range of applications in such diverse fields as digital communications, pattern recognition, biomedical engineering, and financial data analysis, among others. This course aims at an introduction to the BSS problem via an exposition of well-known and established as well as some more recent approaches to its solution. A unified way is followed in presenting the various results so as to more easily bring out their similarities/differences and emphasize their relative advantages/disadvantages. Only a representative sample of the existing knowledge on BSS will be included in this course. The interested readers are encouraged to consult the list of bibliographical references for more details on this exciting and always active research topic.Comment: Tutorial overview of BSS (also presented at SBrT-2001), providing a complete account of the area in early 2000'