Independent component analysis based blind source separation algorithm and its application in the gravity and magnetic signal processing

Geophysical data processing further constrained inversion is evolving progressively prevalent in geoscience domains for three-dimensional modelling and resources evaluation. The process is based on the magnetic and gravity data processing further constrained Cartesian cut cell inversion to discern the maximum of information about HAJJAR deposit in order to calculate its tonnage. This article exhibits data and inversion processing technique for tonnage calculation based on an important geophysical magnetic and gravity surveys of defined extent of HAJJAR region, which presents a great benefit to save time and have accurate and realistic results to a same case. Otherwise, the potential-field signatures of what are regarded to be geologically expressive features are sought within the magnetic and gravity data. The preliminary stage for tonnage calculation was residual anomaly processing and depth estimation of the orebody using spectral analysis method. However, progressing towards extracting the deposit signature, the used method leads to invest the gravity signature of the orebody in adequacy with the magnetic signature. Finally, the tonnage calculation was developed by constrained Cartesian cut cell inversion using Voxi Earth ModellingTM. Obtained results were very important, given their qualitative and quantitative accuracy, which give an added value for the governmental geological and geophysical survey.

The impact of outliers on signal separation performance of an independent component analysis (ICA) algorithm is an important factor when selecting an ICA algorithm. If an ICA estimator has the property of B-robustness, the influence of an extreme point is bounded, leading to good separation performance in the presence of outliers. Since this property is binary, it does not give the degree of influence an outlier has on the separation performance. To address this issue, a Mamdani-type fuzzy inference, based on the location of a potential outlier and on the skewness of the data set, has been developed. It creates an outlier sensitivity map for an ICA algorithm. The implication of this work is a criterion to switch from one ICA algorithm to another in real time, as determined by the algorithms sensitivity to the data set under consideration. This paper describes estimation of the outlier impact on the separation performance of the non-B-robust FastICA algorithm using a Mamdani-type fuzzy inference. In simulations with data sets contaminated by outliers, the FastICA sensitivity map resembles the separation performance measured by the Amari performance index.

Editorial Source separation is not a new problem. We, human beings, as well as many other species, do it unconsciously at every instant of our lives. Our organisms receive a multitude of signals mixed together from the environment, and we are constantly uncovering the relevant ones in order to derive vital information to continue our lives. Other than the biological signals that are occurring at the cell or organ level, there are also various source separation tasks that we consciously do daily. In a crowded underground, room or office, we try to extract what our friend or colleague is telling us among all other speech or audial signals arriving at our ears. Although the source separation problem is handled rather seamlessly by our brains, its implementation in computers has required the development of mathematical models and algorithms. Starting in the 1980s, the problem has been addressed firstly in the context of the cocktail party problem: how to separate a number of speech signals from multichannel mixtures of them. Originally, a simple model of linear mixing was adopted. A solution has been provided to this simplified problem by the independent component analysis algorithm. Later, several other applications have been considered with source separation problems ranging from financial time series analysis to functional magnetic resonance imaging, and from cosmological image separation to music signal separation. The model has been extended to convolutive mixtures and to non-linear mixtures, and variations of the independent component analysis (ICA) algorithm have been utilised. The essence behind independent component analysis is the assumption of statistical independence of the sources. Since the problem is a blind one, that is, we do not know the channel (mixing) characteristics, the mixture model alone represents an ill-posed problem, and we need additional information to resolve the unmixing. The independence assumption provides this additional

The higher-order statistics based independent component analysis (ICA) algorithm can extract natural image features. Based on the maximum likelihood ICA criterion, and using the weighted orthogonal constrained natural gradient, a new ICA algorithm is proposed. Natural image feature extraction simulation results show that, compared with other ICA algorithms, the proposed algorithm has faster convergence rate, most of the extracted basis vectors are localized in space, frequency, and orientation, which can describe the features of the natural images well, and the corresponding coefficients are very sparse, obey stronger super-Gaussian distribution with very high kurtosis.

Our goal is to develop a novel BCI based on an eye movements system employing EEG signals on-line. Most of the analysis on EEG signals has been performed using ensemble averaging approaches. However,It is suitable to analyze raw EEG signals in signal processing methods for BCI. In order to process raw EEG signals, we used independent component analysis(ICA). However, we do not know which ICA algorithms have good performance. It is important to check which ICA algorithms have good performance to develop BCIs. Previous paper presented extraction rate of saccade-related EEG signals by five ICA algorithms and eight window size. However, three ICA algorithms, the FastICA, the NG-FICA and the JADE algorithms, are based on 4th order statistic and AMUSE algorithm has an improved algorithm named SOBI.Therefore, we must re-select ICA algorithms. In this paper, we add new algorithms; the SOBI and the MILCA. The SOBI is an improved algorithm based on the AMUSE and uses at least two covariance matrices at different time steps. The MILCA use the independency based on mutual information. Using the Fast ICA, the JADE, the AMUSE, the SOBI, and the MILCA, we extract saccade-related EEG signals and check extracting rates. Secondly, in order to get more robustness against EOG noise, we use improved FastICA with reference signals and check extracting rates.

As an important factor in the fast fixed-point algorithm of independent component analysis (ICA), noise has a significant influence on the separate performance of ICA. Unfortunately, the traditional algorithm of noisy ICA did not address the influence of impulsive components. Because the sources were signals mixed with impulsive noise, the Gaussian noisy algorithm will be invalid for separating the sources. In general, those measurements that significantly deviate from the normal pattern of sensed data are considered impulses. In this paper, we introduce a non-linear function based on the S-estimator to identify the impulsive components in the observed data. This approach guarantees that the impulse noise can be detected from the observed signal. Furthermore, a threshold for the impulse components and methods to remove impulse noise and reconstruct the signal is proposed. The proposed technique improves the separate performance of the traditional algorithm for Gaussian noisy ICA. With the proposed method, the fast fixed-point algorithm of ICA is more reliable for noisy situations. The simulation results show the effectiveness of the proposed method.

Current analytical techniques applied to functional magnetic resonance imaging (fMRI) data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Here we describe a new method for analyzing fMRI data based on the independent component analysis (ICA) algorithm of Bell and Sejnowski ([1995]: Neural Comput 7:1129-1159). We decomposed eight fMRI data sets from 4 normal subjects performing Stroop color-naming, the Brown and Peterson work/number task, and control tasks into spatially independent components. Each component consisted of voxel values at fixed three-dimensional locations (a component "map"), and a unique associated time course of activation. Given data from 144 time points collected during a 6-min trial, ICA extracted an equal number of spatially independent components. In all eight trials, ICA derived one and only one component with a time course closely matching the time course of 40-sec alternations between experimental and control tasks. The regions of maximum activity in these consistently task-related components generally overlapped active regions detected by standard correlational analysis, but included frontal regions not detected by correlation. Time courses of other ICA components were transiently task-related, quasiperiodic, or slowly varying. By utilizing higher-order statistics to enforce successively stricter criteria for spatial independence between component maps, both the ICA algorithm and a related fourth-order decomposition technique (Comon [1994]: Signal Processing 36:11-20) were superior to principal component analysis (PCA) in determining the spatial and temporal extent of task-related activation. For each subject, the time courses and active regions of the task-related ICA components were consistent across trials and were robust to the addition of simulated noise. Simulated movement artifact and simulated task-related activations added to actual fMRI data were clearly separated by the algorithm. ICA can be used to distinguish between nontask-related signal components, movements, and other artifacts, as well as consistently or transiently task-related fMRI activations, based on only weak assumptions about their spatial distributions and without a priori assumptions about their time courses. ICA appears to be a highly promising method for the analysis of fMRI data from normal and clinical populations, especially for uncovering unpredictable transient patterns of brain activity associated with performance of psychomotor tasks.

We address the problem of Blind Source Separation (BSS) of superimposed signals in situations where one signal has constant or slowly varying intensities at some consecutive locations and at the corresponding locations the other signal has highly varying intensities. Independent Component Analysis (ICA) is a major technique for Blind Source Separation and the existing ICA algorithms fail to estimate the original intensities in the stated situation. We combine the advantages of existing sparse methods and Kernel ICA in our technique, by proposing wavelet packet based sparse decomposition of signals prior to the application of Kernel ICA. Simulations and experimental results illustrate the effectiveness and accuracy of the proposed approach. The approach is general in the way that it can be tailored and applied to a wide range of BSS problems concerning one-dimensional signals and images (two-dimensional signals).

The problem of blind source separation (BSS) has been intensively studied by the signal processing community. The first solutions to deal with BSS were proposed in the 1980's and are founded on the concept of independent component analysis (ICA). More recently, aiming at tackling some limitations of ICA-based methods, much attention has been paid to alternative BSS approaches. In this tutorial, in addition to providing a brief review of the classical BSS framework, we present two research trends in this area, namely source separation over Galois fields and sparse component analysis. For both subjects, we provide an overview of the main criteria, highlighting scenarios that can benefit from these more recent BSS paradigms.

The major challenge facing NMR spectroscopic mixture analysis is the overlapping of signals and the arising impossibility to easily recover the structures for identification of the individual components and to integrate separated signals for quantification. In this paper, various independent component analysis (ICA) algorithms [mutual information least dependent component analysis (MILCA); stochastic non-negative ICA (SNICA); joint approximate diagonalization of eigenmatrices (JADE); and robust, accurate, direct ICA algorithm (RADICAL)] as well as deconvolution methods [simple-to-use-interactive self-modeling mixture analysis (SIMPLISMA) and multivariate curve resolution-alternating least squares (MCR-ALS)] are applied for simultaneous (1)H NMR spectroscopic determination of organic substances in complex mixtures. Among others, we studied constituents of the following matrices: honey, soft drinks, and liquids used in electronic cigarettes. Good quality spectral resolution of up to eight-component mixtures was achieved (correlation coefficients between resolved and experimental spectra were not less than 0.90). In general, the relative errors in the recovered concentrations were below 12%. SIMPLISMA and MILCA algorithms were found to be preferable for NMR spectra deconvolution and showed similar performance. The proposed method was used for analysis of authentic samples. The resolved ICA concentrations match well with the results of reference gas chromatography-mass spectrometry as well as the MCR-ALS algorithm used for comparison. ICA deconvolution considerably improves the application range of direct NMR spectroscopy for analysis of complex mixtures.

We apply the independent component analysis (ICA) algorithm to uncover intrinsic noise in the beam position monitor (BPM) system. Numerical simulations found that ICA is efficient in the BPM noise estimation. The ICA algorithm is applied to the turn-by-turn data at the Relativistic Heavy Ion Collider. We found the distribution of the BPM noise level, which is consistent with the Johnson-Nyquist thermal noise model. The ICA analysis of turn-by-turn data can be used in neuronetwork feasibility of monitoring a storage ring parasitically.

Most algorithms for blind source separation (BSS) or independent component analysis (ICA) assume an equal number of sources as sensors. For multichannel electrophysiological recordings, such as the electroencephalogram (EEG), however, there are often far fewer sources of neurophysiologically relevant activity than the number of sensors. This adds a model order estimation problem to the source separation problem. Conventional estimates of the number of sources are based on the dominant eigenvalues of the data covariance matrix, obtained from principal component analysis (PCA), whose corresponding eigenvectors are also used for prewhitening. It is well known that PCA is susceptible to noise, leading to incorrect model order estimates and data distortion, which in turn limit the accuracy of the source estimates. It is therefore highly desirable to determine the correct number of sources and their spatial topographies directly, without PCA-based data truncation or prewhitening. In this work, we present a stepwise BSS method for extracting only the sources necessary for a sufficiently good least-square fit to the data. This simultaneously yields model order and source estimates, which we examine at different noise levels. We also show how only a few neurophysiologically meaningful components can be extracted from 25-channel ictal EEG.

When the independent sources are known to be nonnegative and well-grounded, which means that they have a non-zero pdf in the region of zero, a few nonnegative independent component analysis (ICA) algorithms have been proposed to separate these positive sources. In this paper, by using the property of skew-symmetry matrix, rigorous convergence proof of a nonnegative ICA algorithm on Stiefel manifold is given. And sufficient convergence conditions are presented. Simulations are employed to confirm our convergence theory. Our techniques may be useful to analyze general ICA algorithms on Stiefel manifold.

Recent advances in intelligence technology have boosted the development of micro- Unmanned Air Vehicles (UAVs) including Sliver Fox, Shadow, and Scan Eagle for various surveillance and reconnaissance applications. These affordable and reusable devices have to fit a series of size, weight, and power constraints. Cameras used on such micro-UAVs are therefore mounted directly at a fixed angle without any motion-compensated gimbals. This mounting scheme has resulted in the so-called <i>jitter effect</i> in which jitter is defined as sub-pixel or small amplitude vibrations. The jitter blur caused by the jitter effect needs to be corrected before any other processing algorithms can be practically applied. Jitter restoration has been solved by various optimization techniques, including Wiener approximation, maximum <i>a-posteriori</i> probability (MAP), etc. However, these algorithms normally assume a spatial-invariant blur model that is not the case with jitter blur. Szu et al. developed a smart real-time algorithm based on auto-regression (AR) with its natural generalization of unsupervised artificial neural network (ANN) learning to achieve restoration accuracy at the sub-pixel level. This algorithm resembles the capability of the human visual system, in which an agreement between the pair of eyes indicates "signal", otherwise, the jitter noise. Using this non-statistical method, for each single pixel, a deterministic blind sources separation (BSS) process can then be carried out independently based on a deterministic minimum of the Helmholtz free energy with a generalization of Shannon's information theory applied to open dynamic systems. From a hardware implementation point of view, the process of jitter restoration of an image using Szu's algorithm can be optimized by pixel-based parallelization. In our previous work, a parallelly structured independent component analysis (ICA) algorithm has been implemented on both Field Programmable Gate Array (FPGA) and Application-Specific Integrated Circuit (ASIC) using standard-height cells. ICA is an algorithm that can solve BSS problems by carrying out the all-order statistical, decorrelation-based transforms, in which an assumption that neighborhood pixels share the same but unknown mixing matrix <b>A</b> is made. In this paper, we continue our investigation on the design challenges of firmware approaches to smart algorithms. We think two levels of parallelization can be explored, including pixel-based parallelization and the parallelization of the restoration algorithm performed at each pixel. This paper focuses on the latter and we use ICA as an example to explain the design and implementation methods. It is well known that the capacity constraints of single FPGA have limited the implementation of many complex algorithms including ICA. Using the reconfigurability of FPGA, we show, in this paper, how to manipulate the FPGA-based system to provide extra computing power for the parallelized ICA algorithm with limited FPGA resources. The synthesis aiming at the pilchard re-configurable FPGA platform is reported. The pilchard board is embedded with single Xilinx VIRTEX 1000E FPGA and transfers data directly to CPU on the 64-bit memory bus at the maximum frequency of 133MHz. Both the feasibility performance evaluations and experimental results validate the effectiveness and practicality of this synthesis, which can be extended to the spatial-variant jitter restoration for micro-UAV deployment.

Independent Component Analysis (ICA) is a method for solving blind source separation problems. Because ICA only needs weak assumptions to estimate the unknown sources from only the observed signals, it is suitable for Electroencephalography (EEG) analysis. A serious disadvantage of the traditional ICA algorithms is that their results often fluctuate and do not converge to the unique and globally optimal solution at each run. It is because there are many local optima and permutation ambiguities. We have recently proposed a new ICA algorithm named the ordering ICA, a simple extension of Fast ICA. The ordering ICA is theoretically guaranteed to extract the independent components in the unique order and avoids the local optima in practice. This paper investigated the usefulness of the ordering ICA in EEG analysis. Experiments showed that the ordering ICA could give unique solutions for the signals with large non-Gaussianity, and the ease of parallelization could reduce computation time.