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We present a novel method to extract classification features from functional magnetic resonance imaging (fMRI) data collected at rest or during the performance of a task. By combining a two-level feature identification scheme with kernel principal component analysis (KPCA) and Fisher's linear discriminant analysis (FLD), we achieve high classification rates(More)
We introduce a framework based on Wirtinger calculus for nonlinear complex-valued signal processing such that all computations can be directly carried out in the complex domain. The two main approaches for performing independent component analysis, maximum likelihood, and maximization of non-Gaussianity-which are intimately related to each other-are studied(More)
In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using(More)
We introduce a framework for complex-valued signal processing such that all computations can be directly carried out in the complex domain. The framework, based on an elegant result due to Brandwood, allows for easy derivation of many complex-valued algorithms and their efficient analyses. We demonstrate its application to derivation of relative gradient(More)
Complex-valued signals arise frequently in applications as diverse as communications, radar, and biomedicine, as most practical modulation formats are of complex type and applications such as radar and magnetic resonance imaging (MRI) lead to data that are inherently complex valued. When the processing has to be done in a transform domain such as Fourier or(More)
We derive a class of algorithms for independent component analysis (ICA) based on maximum likelihood (ML) estimation and perform stability analysis of natural gradient ML ICA with and without the constraint for unitary demixing matrix. In the process, we demonstrate how Wirtinger calculus facilitates derivations, and most importantly, performing(More)
We present two algorithms for independent component analysis of complex-valued signals based on the maximization of absolute value of kurtosis and establish their properties. Both the algorithm derivation and the analysis are carried out directly in the complex domain, without the use of complex-to-real mappings as the cost function satisfies Brandwood's(More)
In this study, we investigate the physical and chemical properties of waste-activated sludge after treatment with microwave irradiation. The results indicate that microwave energy and contact time strongly influence the physical and chemical properties of sludge. According to the settling velocity and particle size measurements, the microwave energy of 900(More)
We describe a framework based on Wirtinger calculus for adaptive signal processing that enables efficient derivation of algorithms by directly working in the complex domain and taking full advantage of the power of complex-domain nonlinear processing. We establish the basic relationships for optimization in the complex domain and the real-domain(More)
Independent component analysis (ICA) has proven quite useful for the analysis of real world datasets such as functional resonance magnetic imaging (fMRI) data, where the underlying nature of the data is hard to model. It is particularly useful for the analysis of fMRI data in its native complex form since very little is known about the nature of phase.(More)