Complex ICA Using Nonlinear Functions

ICA of full complex-valued fMRI data using phase information of spatial maps

“…Note that the analysis was restricted to a portion (the posterior half) of the brain due to the noisy nature of whole-brain data. The efforts of follow-up research were mainly directed toward development of complexvalued ICA algorithms for estimating the TC and SM components efficiently Calhoun et al, 2004;Calhoun and Adali, 2006b;Adali and Calhoun, 2007;Novey and Adali, 2008;Adali et al, 2008;Li and Adali, 2008;Chen and Lin, 2008) and order selection for complex-valued fMRI data (Wang et al, 2008).…”

Efficient Variant of Noncircular Complex FastICA Algorithm for the Blind Source Separation of Digital Communication Signals

“…where V 1 → E[|s 1 | 2 g(|s 1 | 2 ) − g(|s 1 | 2 ) − |s 1 | 2 g (|s 1 | 2 )]I N −1 , I N −1 is a (N − 1) × (N − 1) dimensional identity matrix, V 2 → −E[s * 2 1 g (|s 1 | 2 )]E(s −1 s T −1 ), u converges to a normal distribution variable with zero mean, covariance V 3 = {E[|s 1 | 2 g 2 (|s 1 | 2 )] − E 2 [|s 1 | 2 g(|s 1 …”

“…where a 1 = E[|s 1 | 2 g(|s 1 | 2 )−g(|s 1 | 2 ) − |s 1 | 2 g (|s 1 | 2 )], a 2 = −E[s * 2 1 g (|s 1 | 2 )]E(s 2 1 ), a 3 = E[|s 1 | 2 g 2 (|s 1 | 2 )] − E 2 [|s 1 | 2 g(|s 1 …”

Efficient Optimization of Reference-Based Negentropy for Noncircular Sources in Complex ICA

“…In [25], using nonlinear functions to approximate the negentropy for a more general case of noncircular sources, Novey extends the work of Bingham [3] by deriving a new fixedpoint algorithm that utilizes the information in a pseudo-covariance matrix. In [26], gradient-descent and quasi-Newton algorithms are derived for noncircular sources based on the complex analytic nonlinear functions proposed in [1]. In [19], a new approach is introduced for correlated noncircular sources that uses only second-order statistics and takes the correlation structure fully into account; in addition, a parametric entropy rate estimator is proposed using a linear autoregressive (AR) model.…”