المؤلفون: Basiri, Shahab¹ shahab.basiri@aalto.fi, Ollila, Esa¹, Koivunen, Visa¹

المصدر: Signal Processing. Sep2017, Vol. 138, p53-62. 10p.

مصطلحات موضوعية: *FIXED point theory, *INFERENTIAL statistics, *ELECTROENCEPHALOGRAPHY, *STATISTICAL bootstrapping, *FUNCTIONAL magnetic resonance imaging

مستخلص: In this paper, we develop low complexity and stable bootstrap procedures for FastICA estimators. Our bootstrapping techniques allow for performing cost efficient and reliable bootstrap-based statistical inference in the ICA model. Performing statistical inference is needed to quantitatively assess the quality of the estimators and testing hypotheses on mixing coefficients in the ICA model. The developed bootstrap procedures stem from the fast and robust bootstrap (FRB) method [1], which is applicable for estimators that may be found as solutions to fixed-point (FP) equations. We first establish analytical results on the structure of the weighted covariance matrix involved in the FRB formulation. Then, we exploit our analytical results to compute the FRB replicas at drastically reduced cost. The developed enhanced FRB method (EFRB) for FastICA permits using bootstrap-based statistical inference in a variety of applications (e.g., EEG, fMRI) in which ICA is commonly applied. Such an approach has not been possible earlier due to incurred substantial computational efforts of the conventional bootstrap. Our simulation studies compare the complexity and numerical stability of the proposed methods with the conventional bootstrap method. We also provide an example of utilizing the developed bootstrapping techniques in identifying equipotential lines of the brain dipoles from electroencephalogram (EEG) recordings. [ABSTRACT FROM AUTHOR]

المؤلفون: Ollila, Esa^1,2, Koivunen, Visa² visa@wooster.hut.fi

المصدر: Signal Processing. Apr2009, Vol. 89 Issue 4, p365-377. 13p.

مصطلحات موضوعية: *DIGITAL signal processing, *RANDOM variables, *MULTIVARIATE analysis, *ROBUST control, *ANALYSIS of covariance, *ESTIMATION theory

مستخلص: Abstract: An extension of the whitening transformation for complex random vectors, called the generalized uncorrelating transformation (GUT), is introduced. GUT is a generalization of the strong-uncorrelating transform [J. Eriksson, V. Koivunen, Complex-valued ICA using 2nd-order statistics, in: Proceedings of the IEEE Workshop on Machine Learning for Signal Processing (MLSP’04), Sao Luis, Brazil, 2004] based upon generalized estimators of the covariance and pseudo-covariance matrix, called the scatter matrix and spatial pseudo-scatter matrix, respectively. Depending on the selected scatter and spatial pseudo-scatter matrix, GUT estimators can have largely different statistical properties. Special emphasis is put on robust GUT estimators. We show that GUT is a separating matrix estimator for complex-valued independent component analysis (ICA) when at most one source random variable possess circularly symmetric distribution and sources do not have identical distribution. In the context of ICA, our approach is computationally attractive as it is based on straightforward matrix computations. Simulations and examples are used to confirm reliable performance of our method. [Copyright &y& Elsevier]

المؤلفون: Muma, Michael¹ (AUTHOR), Ollila, Esa² (AUTHOR), Pascal, Frédéric³ (AUTHOR)

المصدر: Signal Processing. May2021, Vol. 182, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *DATA science, *SIGNAL processing, *FISHER information, *REGRESSION analysis, *TIME series analysis, *MULTIPLE imputation (Statistics)

المؤلفون: Mecklenbräuker, Christoph F.¹ (AUTHOR) cfm@tuwien.ac.at, Gerstoft, Peter² (AUTHOR), Ollila, Esa³ (AUTHOR), Park, Yongsung² (AUTHOR)

المصدر: Signal Processing. Jul2024, Vol. 220, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *STANDARD deviations, *GAUSSIAN distribution

مستخلص: A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t -distribution (MVT) with ν degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and ϵ -contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian array data. • SBL algorithm with general loss function for DOA M-estimation. • The CES data model includes Gaussian data as special case. • Robust and sparse DOA M-estimator is insensitive to heavy tails, outliers, and unknown source correlations. [ABSTRACT FROM AUTHOR]

المؤلفون: Ollila, Esa¹ esollila@wooster.hut.fi, Oja, Hannu², Koivunen, Visa¹

المصدر: Computational Statistics & Data Analysis. Mar2008, Vol. 52 Issue 7, p3789-3805. 17p.

مصطلحات موضوعية: *UNIVERSAL algebra, *CALCULUS of operations, *MATRICES (Mathematics), *STATISTICS

مستخلص: Abstract: It is shown that any pair of scatter and spatial scatter matrices yields an estimator of the separating matrix for complex-valued independent component analysis (ICA). Scatter (resp. spatial scatter) matrix is a generalized covariance matrix in the sense that it is a positive definite hermitian matrix functional that satisfies the same affine (resp. unitary) equivariance property as does the covariance matrix and possesses an additional IC-property, namely, it reduces to a diagonal matrix at distributions with independent marginals. Scatter matrix is used to decorrelate the data and the eigenvalue decomposition of the spatial scatter matrix is used to find the unitary mixing matrix of the uncorrelated data. The method is a generalization of the FOBI algorithm, where a conventional covariance matrix and a certain fourth-order moment matrix take the place of the scatter and spatial scatter matrices, respectively. Emphasis is put on estimators employing robust scatter and spatial scatter matrices. The proposed approach is one among the computationally most attractive ones, and a new efficient algorithm that avoids decorrelation of the data is also proposed. Moreover, the method does not rely upon the commonly made assumption of complex circularity of the sources. Simulations and examples are used to confirm the reliable performance of our method. [Copyright &y& Elsevier]

المؤلفون: Remes, Jukka J.^1,2 jukka.remes@iki.fi, Abou Elseoud, Ahmed¹, Ollila, Esa^3,4, Haapea, Marianne^1,5, Starck, Tuomo¹, Nikkinen, Juha¹, Tervonen, Osmo¹, Silven, Olli²

المصدر: Magnetic Resonance Imaging (0730725X). Oct2013, Vol. 31 Issue 8, p1338-1348. 11p.

مصطلحات موضوعية: *VOXEL-based morphometry, *PRINCIPAL components analysis, *FUNCTIONAL magnetic resonance imaging, *SLIDING mode control, *BRAIN physiology, *ANALYSIS of variance

مستخلص: Abstract: Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations. [Copyright &y& Elsevier]

المؤلفون: Miettinen, Jari¹ (AUTHOR), Vorobyov, Sergiy A.¹ (AUTHOR), Ollila, Esa¹ (AUTHOR) esa.ollila@aalto.fi

المصدر: Signal Processing. Dec2021, Vol. 189, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *SIGNAL processing, *REPRESENTATIONS of graphs, *INDEPENDENT component analysis, *SIGNAL filtering

مستخلص: • We formulate graph error models for the adjacency matrix, which help to quantify the deviation from the true matrix using a few parameters. • We study the structural effects of the proposed error models on the adjacency matrix. • The effects of different type of errors in adjacency matrix specification are illustrated in filtering of graph signal and ICA of graph signals. The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little attention has been paid to modelling such errors in the adjacency matrix, and studying their effects on GSP methods. However, modelling errors in the adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically when possible and numerically, the graph error effect on the performance of GSP methods in different types of problems such as filtering of graph signals and independent component analysis of graph signals (graph decorrelation). [ABSTRACT FROM AUTHOR]

المؤلفون: Veshki, Farshad G.¹ (AUTHOR) farshad.ghorbaniveshki@aalto.fi, Ouzir, Nora² (AUTHOR) nora.ouzir@centralesupelec.fr, Vorobyov, Sergiy A.¹ (AUTHOR) sergiy.vorobyov@aalto.fi, Ollila, Esa¹ (AUTHOR) esa.ollila@aalto.fi

المصدر: Signal Processing. Nov2022, Vol. 200, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *IMAGE fusion, *FEATURE extraction, *SPARSE approximations, *PEARSON correlation (Statistics)

مستخلص: • A general learning-based decomposition model suitable for fusing images from various imaging modalities is proposed. • The multimodal images are decomposed into correlated and uncorrelated components. • A CDL method based on simultaneous sparse approximation is proposed for estimating the correlated features. • The uncorrelated components are estimated using a Pearson correlation-based constraint. This paper presents a multimodal image fusion method using a novel decomposition model based on coupled dictionary learning. The proposed method is general and can be used for a variety of imaging modalities. In particular, the images to be fused are decomposed into correlated and uncorrelated components using sparse representations with identical supports and a Pearson correlation constraint, respectively. The resulting optimization problem is solved by an alternating minimization algorithm. Contrary to other learning-based fusion methods, the proposed approach does not require any training data, and the correlated features are extracted online from the data itself. By preserving the uncorrelated components in the fused images, the proposed fusion method significantly improves on current fusion approaches in terms of maintaining the texture details and modality-specific information. The maximum-absolute-value rule is used for the fusion of correlated components only. This leads to an enhanced contrast-resolution without causing intensity attenuation or loss of important information. Experimental results show that the proposed method achieves superior performance in terms of both visual and objective evaluations compared to state-of-the-art image fusion methods. [ABSTRACT FROM AUTHOR]