Joint Approximate Diagonalization Of Eigenmatrices Research Articles

Identification of galaxy clusters in cosmic microwave background maps using the Sunyaev-Zel’dovich effect

The Planck satellite was launched in 2009 by the European Space Agency to study the properties of the cosmic microwave background (CMB). An expected result of the Planck data analysis is the distinction of the various contaminants of the CMB signal. Among these contaminants is the Sunyaev-Zel'dovich (SZ) effect, which is caused by the inverse Compton scattering of CMB photons by high energy electrons in the intracluster medium of galaxy clusters. We modify a public version of the JADE (Joint Approximate Diagonalization of Eigenmatrices) algorithm, to deal with noisy data, and then use this algorithm as a tool to search for SZ clusters in two simulated datasets. The first dataset is composed of simple "homemade" simulations and the second of full sky simulations of high angular resolution, available at the LAMBDA (Legacy Archive for Microwave Background Data Analysis) website. The process of component separation can be summarized in four main steps: (1) pre-processing based on wavelet analysis, which performs an initial cleaning (denoising) of data to minimize the noise level; (2) the separation of the components by JADE; (3) the calibration of the recovered SZ map; and (4) the identification of the positions and intensities of the clusters using the SExtractor software. The results show that our JADE-based algorithm is effective in identifying the position and intensity of the SZ clusters, with the purities being higher then 90% for the extracted "catalogues". This value changes slightly according to the characteristics of noise and the number of components included in the input maps. The main highlight of our developed work is the effective recovery rate of SZ sources from noisy data, with no a priori assumptions. This powerful algorithm can be easily implemented and become an interesting complementary option to the "matched filter" algorithm widely used in SZ data analysis.

Hyperspectral Blind Unmixing and Multiple Target Detection Using Linear Mixture Model

In this paper a blind source separation technique Joint Approximate Diagonalization of Eigen-matrices (JADE) is investigated to unmixing and multiple target detection for hyperspectral imagery data. Our targeted minerals are Alunite, Buddingtonite, Calcite and Kaolinite in ‘Cuprite’ scene data that has been widely used for research experiments in hyperspectral imagery. A comparative study is conducted to show the effectiveness of the JADE with Vertex Component Analysis. The results are evaluated with both full and reduced bands.

Analysis of Superimposed Ultrasonic Guided Waves in Long Bones by the Joint Approximate Diagonalization of Eigen-matrices Algorithm

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones.

Comparison of Blind Source Separation Methods in Fast Somatosensory-Evoked Potential Detection

Blind source separation (BSS) is a promising method for extracting somatosensory-evoked potential (SEP). Although various BSS algorithms are available for SEP extraction, few studies have addressed the performance differences between them. In this study, we compared the performance of a number of typical BSS algorithms on SEP extraction from both computer simulations and clinical experiment. The algorithms we compared included second-order blind identification, estimation of signal parameters via rotation invariance technique, algorithm for multiple unknown signals extraction, joint approximate diagonalization of eigenmatrices, extended infomax, and fast independent component analysis. The performances of these BSS algorithms were determined by the correlation coefficients between the true and the extracted SEP signals. There were significant differences in the performances of the various BSS algorithms in a simulation study. In summary, second-order blind identification using six covariance matrix denoting SOBI6 was recommended as the most appropriate BSS method for fast SEP extraction from noisy backgrounds.

Blind channel estimation based on maximizing the eigenvalue spread of cumulant matrices in (2 × 1) Alamouti's coding schemes

AbstractThe popular Alamouti orthogonal space time code attains full transmit diversity in multiple antenna systems. This paper addresses the problem of blind channel identification in (2 × 1) Alamouti coded systems. Under the assumption of independent symbol substreams, the channel can be estimated from the eigendecomposition of matrices composed of second‐ or higher‐order statistics (cumulants) of the received signal. The so‐called joint approximate diagonalization of eigenmatrices (JADE) method for blind source separation via independent component analysis is optimal in that it tries to simultaneously diagonalize a full set of fourth‐order cumulant matrices. To reduce computational complexity, we perform the eigenvalue decomposition of a single cumulant matrix, which is judiciously chosen by maximizing its expected eigenvalue spread. Simulation results show that the resulting technique outperforms existing blind Alamouti channel estimation methods and achieves a performance close to JADE's at a fraction of the computational cost. Copyright © 2010 John Wiley & Sons, Ltd.

On the Performance Analysis of the ICA Algorithms with Maternal and Fetal ECG signals Inputs and Contaminated Noises

This paper evaluates the performance of some major Independent Component Analysis (ICA) algorithms like Cardoso’s Joint Approximate Diagonalization of Eigen matrices (JADE), Comon’s algorithm and Optimized Generalized Weighted Estimator (OGWE) ICA algorithm in a biomedical blind source separation problem. Independent signals representing Fetal ECG (FECG) and Maternal ECG (MECG) are generated and then mixed linearly in the presence of white or pink noise to simulate a recording of electrocardiogram. While ICA has been used to extract FECG, very little literature is available on its performance in clinical environment. So there is a need to evaluate performance of these algorithms in Biomedical. To quantify the performance of ICA algorithms, two scenarios, i.e., (a) different amplitude ratios of simulated maternal and fetal ECG signals, (b) different values of additive white Gaussian noise or pink noise, were investigated. Higher order and second order performances were measured by performance index and signal-to-error ratio respectively. The selected ICA algorithms separate the white and pink noises equally well. This paper reports on the performance of the ICA algorithms.

An MSE-Based Method to Avoid Permutation/Gain Indeterminacy in Frequency-Domain Blind Source Separation

This paper presents a novel technique for separating convolutive mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. This problem is solved in the frequency domain by transforming the convolutive mixture into several instantaneous mixtures which are independently separated using blind source separation (BSS) algorithms. First, the instantaneous mixture at one frequency is solved using the joint approximate diagonalization of eigenmatrices (JADE) technique, and the other mixtures are then separated using the mean squared error (MSE) criterion. As a special case of this method, we consider the separation of non-Gaussian temporally white signals transmitted in blocks with zero padding between them.

Nonorthogonal Joint Diagonalization by Combining Givens and Hyperbolic Rotations

A new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications. This algorithm is an extension of the Jacobi-like algorithm first proposed in the joint approximate diagonalization of eigenmatrices (JADE) method for orthogonal joint diagonalization. The improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix. This target matrix is constructed iteratively by successive multiplications of not only Givens rotations but also hyperbolic rotations and diagonal matrices. The algorithm performance, evaluated on synthetic data, compares favorably with existing methods in terms of speed of convergence and complexity.

Preprocessing Methods of Raman Spectra for Source Extraction on Biomedical Samples: Application on Paraffin-Embedded Skin Biopsies

Raman spectra are classically modeled as a linear mixing of spectra of molecular constituents of the analyzed sample. Source separation methods are thus well suited to estimate these constituent spectra. However, physical distortions due to the instrumentation and biological nature of samples add nonlinearities to the Raman spectra model. These distortions are dark current, detector and optic responses, fluorescence background, and peak misalignment and peak width heterogeneity. The source separation results are thus deteriorated by these effects. We propose to develop specific preprocessing steps to correct these distortions and to retrieve a linear model. The benefits brought by these steps are studied by the application of two different source separation methods named joint approximate diagonalization of eigenmatrices and maximum likelihood positive source separation after the application of each step on a dataset acquired on a paraffin-embedded human skin biopsy. The efficacy of these methods to separate Raman spectra is also discussed.

Theoretical studies and efficient algorithm of semi-blind ICI equalization for OFDM

The intercarrier interference (ICI) due to the Doppler frequency shift, sampling clock offset, time-varying multipath fading and local oscillator frequency offset becomes the major difficulty for the data transmission via the wireless orthogonal frequency division multiplexing (OFDM) systems. The existing ICI mitigation schemes involve the frequency-domain channel estimation/equalization or the additional coding and therefore require the pilot symbols which reduce the throughput. The frequency-domain channel estimation/equalization relies on the huge matrix inversion with high computational complexity especially for the OFDM technologies possessing many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). In our previous work, we proposed a semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm and empirically showed that the proposed method significantly improved the symbol error rates for QPSK- and 16QAM-OFDM systems. In this paper, we discuss the sufficient condition for the theoretical ICI equalizability and also propose an alternative semi-blind ICI equalization method based on the joint approximate diagonalization of eigen-matrices (JADE) algorithm, which is much more computationally efficient than our previous method.

Prétraitements et méthodes de séparation de sources pour l’analyse des spectres Raman issus d’échantillons biologiques

Raman spectroscopy is a useful tool to investigate the molecular composition of biological samples. Source separation methods can be used to efficiently separate dense information recorded by Raman spectra. Distorting effects such as fluorescence background, peak misalignment or peak width heterogeneity break the linear generative model required by the source separation methods. Preprocessing steps are needed to compensate these deforming effects and make recorded Raman spectra fit the linear generative model of source separation methods. We show in this paper how efficiency of source separation methods is deeply dependent on preprocessing steps applied to raw dataset. Resulting improvements are illustrated through the study of the numerical dewaxing of Raman signal of a human skin biopsy. The applied source separation methods are a classical independent component analysis (ICA) algorithm named joint approximate diagonalization of eigenmatrices (JADE), and two positive source separation methods called non-negative matrix factorization (NMF) and maximum likelihood positive source separation (MLPSS).

Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.

Independent Component Analysis in the Study of Focal Seizures

Independent component analysis (ICA) is a novel technique that can separate statistically independent elements from complex signals. It has demonstrated its utility in separating artifacts and analyzing interictal discharges in EEG. ICA has been used recently in ictal recordings, showing the possibility of isolating the ictal activity. The goal of our study was to analyze focal seizures with ICA, decomposing the elements of the seizures to understand their genesis and propagation, and to differentiate between various types of focal seizures. We studied 26 focal seizures of temporal, frontal, or parietal origin. Only seizures with suspected focal onset were included in the study. The EEG recordings were acquired by using standard video-EEG equipment, with scalp electrodes. All the off-line analysis was carried out on a PC by means of specific software developed in the Matlab environment. ICA components were calculated with the use of the JADE (Joint Approximate Diagonalization of Eigen-matrices) algorithm. The decomposition of the seizures varied according to the EEG seizure pattern. In the seizures with focal rhythmic theta slow or sharp waves, the rhythmic activity was separated into one to five components, having an initial component with a clear concordance with the focus, whereas the others had an onset a few milliseconds later and corresponded to neighboring areas. In the 6 frontal seizures with regional rhythmic low voltage fast activity, 4 to 10 components were found, practically with a simultaneous timing, having a frontal distribution. In the three frontal seizures with a diffuse attenuation of the EEG signal, it was not possible to differentiate components of cerebral origin from the components of muscle artifact. ICA is an interesting tool to study the nature of focal seizures. The results depend on the EEG pattern. In the seizures with a clear EEG focal pattern, ICA may be useful to separate components of the ictal onset from the propagated activity.

A Novel Image Recovery Algorithm for Visible Watermarked Images

A novel image recovery algorithm for removing visible watermarks is presented. Independent component analysis (ICA) is utilized to separate source images from watermarked and reference images. Three independent component analysis approaches are examined in the proposed algorithm, which includes joint approximate diagonalization of eigenmatrices, second-order blind identification, and FastICA. Moreover, five different visible watermarking methods to embed uniform and linear-gradient watermarks are implemented. The experimental results show that visible watermarks are successfully removed, and that the proposed algorithm is independent of both the adopted ICA approach and the visible watermarking method. In the final experiment, several public domain images sourced from various websites are tested. The results of this study demonstrate that the proposed algorithm can blindly and successfully remove the visible watermarks without knowing the watermarking methods in advance

Independent-component analysis for hyperspectral remote sensing imagery classification

We investigate the application of independent-component analysis (ICA) to remotely sensed hyperspectral image classification. We focus on the performance of two well-known and frequently used ICA algorithms: joint approximate diagonalization of eigenmatrices (JADE) and FastICA; but the proposed method is applicable to other ICA algorithms. The major advantage of using ICA is its ability to classify objects with unknown spectral signatures in an unknown image scene, i.e., unsupervised classification. However, ICA suffers from computational expensiveness, which limits its application to high-dimensional data analysis. In order to make it applicable or reduce the computation time in hyperspectral image classification, a data-preprocessing procedure is employed to reduce the data dimensionality. Instead of using principal-component analysis (PCA), a noise-adjusted principal-components (NAPC) transform is employed for this purpose, which can reorganize the original data with respect to the signal-to-noise ratio, a more appropriate image-ranking criterion than variance in PCA. The experimental results demonstrate that the major principal components from the NAPC transform can better maintain the object information in the original data than those from PCA. As a result, an ICA algorithm can provide better object classification.

Independent Component Analysis as a Tool to Eliminate Artifacts in EEG: A Quantitative Study

Independent component analysis (ICA) is a novel technique that calculates independent components from mixed signals. A hypothetical clinical application is to remove artifacts in EEG. The goal of this study was to apply ICA to standard EEG recordings to eliminate well-known artifacts, thus quantifying its efficacy in an objective way. Eighty samples of recordings with spikes and evident artifacts of electrocardiogram (EKG), eye movements, 50-Hz interference, muscle, or electrode artifact were studied. ICA components were calculated using the Joint Approximate Diagonalization of Eigen-matrices (JADE) algorithm. The signal was reconstructed excluding those components related to the artifacts. A normalized correlation coefficient was used as a measure of the changes caused by the suppression of these components. ICA produced an evident clearing-up of signals in all the samples. The morphology and the topography of the spike were very similar before and after the removal of the artifacts. The correlation coefficient showed that the rest of the signal did not change significantly. Two examiners independently looked at the samples to identify the changes in the morphology and location of the discharge and the artifacts. In conclusion, ICA proved to be a useful tool to clean artifacts in short EEG samples, without having the disadvantages associated with the digital filters. The distortion of the interictal activity measured by correlation analysis was minimal.

A generalization of joint-diagonalization criteria for source separation

In the field of blind source separation, joint-diagonalization-based approaches constitute an important framework, leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices (JADE) and simultaneous third-order tensor diagonalization (STOTD) algorithms. However, they are often restricted to the case of cumulants of order four. In this paper, we extend the results leading to JADE and STOTD to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results. This also leads us to generalize some links between contrast functions and joint-diagonalization criteria on which these algorithms are based. In turn, one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast. Moreover, for the two generalized JADE and STOTD contrasts, the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression, whatever the cumulant order. Finally, some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint-diagonalization of cumulant matrices.

A least squares approach to blind beamforming

We present a least squares approach to blind beamforming. Two estimation criteria are derived. One turns out to coincide with the Comon (1990, 1994) criterion, whereas the other is a computationally simpler criterion similar in nature to the joint approximate diagonalization of eigenmatrices (JADE) criterion.