Pedro A. Rodriguez

De-noising, phase ambiguity correction and visualization techniques for complex-valued ICA of group fMRI data

Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity both for data-driven techniques, such as independent component analysis (ICA), and for model-driven techniques. The promise of an increase in sensitivity and specificity in clinical studies, provides a powerful motivation for utilizing both the phase and magnitude data; however, the unknown and noisy nature of the phase poses a challenge. In addition, many complex-valued analysis algorithms, such as ICA, suffer from an inherent phase ambiguity, which introduces additional difficulty for group analysis. We present solutions for these issues, which have been among the main reasons phase information has been traditionally discarded, and show their effectiveness when used as part of a complex-valued group ICA algorithm application. The methods we present thus allow the development of new fully complex data-driven and semi-blind methods to process, analyze, and visualize fMRI data.We first introduce a phase ambiguity correction scheme that can be either applied subsequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. We also present a Mahalanobis distance-based thresholding method, which incorporates both magnitude and phase information into a single threshold, that can be used to increase the sensitivity in the identification of voxels of interest. This method shows particular promise for identifying voxels with significant susceptibility changes but that are located in low magnitude (i.e. activation) areas. We demonstrate the performance gain of the introduced methods on actual fMRI data.

Application of Independent Component Analysis With Adaptive Density Model to Complex-Valued fMRI Data

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. Phase information has been discarded in most analyses as it is particularly noisy. In this paper, we show that a complex ICA approach using a flexible nonlinearity that adapts to the source density is the more desirable one for performing ICA of complex fMRI data compared to those that use fixed nonlinearity, especially when noise level is high. By adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of spatial maps and the task-related time courses, especially for the estimation of phase of the time course. We also define a procedure for analysis and visualization of complex-valued fMRI results, which includes the construction of bivariate t-maps for multiple subjects and a complex-valued ICASSO scheme for evaluating the consistency of ICA algorithms.

An effective decoupling method for matrix optimization and its application to the ICA problem

Matrix optimization of cost functions is a common problem. Construction of methods that enable each row or column to be individually optimized, i.e., decoupled, are desirable for a number of reasons. With proper decoupling, the convergence characteristics such as local stability can be improved. Decoupling can enable density matching in applications such as independent component analysis (ICA). Lastly, efficient Newton algorithms become tractable after decoupling. The most common method for decoupling rows is to reduce the optimization space to orthogonal matrices. Such restrictions can degrade performance. We present a decoupling procedure that uses standard vector optimization procedures while still admitting nonorthogonal solutions. We utilize the decoupling procedure to develop a new decoupled ICA algorithm that uses Newton optimization enabling superior performance when the sample size is limited.

Quality Map Thresholding for De-noising of Complex-Valued fMRI Data and Its Application to ICA of fMRI

Although functional magnetic resonance imaging (fMRI) data are acquired as complex-valued images, traditionally most fMRI studies only use the magnitude of the data. FMRI analysis in the complex domain promises to provide more statistically significant information; however, the noisy nature of the phase poses a challenge for successful study of fMRI by complex-valued signal processing algorithms. In this paper, we introduce a physiologically motivated de-noising method that uses phase quality maps to successfully identify and eliminate noisy areas in the fMRI data so they can be used in individual and group studies. Additionally, we show how the developed de-noising method improves the results of complex-valued independent component analysis of fMRI data, a very successful tool for blind source separation of biomedical data.

Flexible complex ICA of fMRI data

Data-driven analysis methods, in particular independent component analysis (ICA) has proven quite useful for the analysis of functional magnetic imaging (fMRI) data. In addition, by enabling one to work in its native, complex form, complex-valued ICA algorithms provide better estimation performance compared to the traditional approach that uses only the magnitude data. In the complex domain, circularity has been a common assumption even though most data acquisition methods collect fMRI data that end up being noncircular when saved in complex form. In this paper, we show that a complex ICA approach that does not assume circularity and also adapts to the source density is the more desirable one for performing ICA of complex fMRI data. We show that by adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of the task-related time courses and in the spatial activation.

General Non-Orthogonal Constrained ICA

Constrained independent component analysis (C-ICA) algorithms have been an effective way to introduce prior information into the ICA framework. The work in this area has focus on adding constraints to the objective function of algorithms that assume an orthogonal demixing matrix. Orthogonality is required in order to decouple-isolate-the constraints applied for each individual source. This assumption limits the optimization space and therefore the separation performance of C-ICA algorithms. We generalize the existing C-ICA framework by using a novel decoupling method that preserves the larger optimization space for the demixing matrix. In addition, this framework allows for the constraining of either the sources or the mixing coefficients. A constrained version of the extended Infomax algorithm is used as an example to show the benefits obtained from the non-orthogonal constrained framework we introduce.

Phase correction and denoising for ICA of complex FMRI data

Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity of the analysis both for data driven techniques such as independent component analysis (ICA) and for model-driven techniques; however, the noisy nature of the phase poses a challenge for successful study of fMRI data. In addition, for complex ICA, the inherent scaling ambiguity, which has a phase term, introduces additional difficulty for group analysis and visualization of the results. In this paper, we address these issues, which have been among the main reasons phase information has been traditionally discarded and introduce a phase correction scheme that can be either applied subsequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. In addition, we introduce methods for visualization of the analysis results as well as preprocessing the complex fMRI data to mitigate the effects of noise in the phase which are not limited to ICA algorithms. We demonstrate the successful application of the methods using actual fMRI data.

Quality map thresholding for de-noising of complex-valued fMRI data and its application to ICA of fMRI

Although functional magnetic resonance imaging (fMRI) data are acquired as complex-valued images, traditionally most fMRI studies only use the magnitude of the data. FMRI analysis in the complex domain promises to provide more statistically significant information; however, the noisy nature of the phase poses a challenge for successful study of fMRI by complex-valued signal processing algorithms. In this paper, we introduce a physiologically motivated de-noising method that uses phase quality maps and demonstrate its effectiveness in successfully identifying and eliminating noisy areas in the fMRI data. Additionally, we show how the developed de-noising method improves the results of complex-valued independent component analysis of fMRI data, a very successful tool for blind source separation of biomedical data.

General Nonunitary Constrained ICA and its Application to Complex-Valued fMRI Data

Constrained independent component analysis (C-ICA) algorithms provide an effective way to introduce prior information into the complex- and real-valued ICA framework. The work in this area has focus on adding constraints to the objective function of algorithms that assume a unitary demixing matrix. The unitary condition is required in order to decouple-isolate-the constraints applied for each individual source. This assumption limits the optimization space and, therefore, the separation performance of C-ICA algorithms. We generalize the existing C-ICA framework by using a novel decoupling method that preserves the larger optimization space for the demixing matrix. This framework allows for the constraining of either the sources or the mixing coefficients. A constrained version of the nonunitary entropy bound minimization algorithm is introduced and applied to actual complex-valued fMRI data. We show that constraining the mixing parameters using a temporal constraint improves the estimation of the spatial map and timecourses of task-related components.

Complex-valued analysis and visualization of fMRI data for event-related and block-design paradigms

Independent Component Analysis (ICA) has been noted to be promising for the study of functional magnetic resonance imaging (fMRI) data also in its native complex-valued form. In this paper, we demonstrate the first successful application of group ICA to complex-valued fMRI data of an event-related paradigm. We show that networks associated with event-related responses as well as intrinsic fluctuations of hemodymamic activity can be extracted for data collected during an auditory oddball paradigm. The intrinsic networks are of particular interest due to their potential to study cognitive function and mental illness, including schizophrenia. More importantly, we show that analysis of fMRI data in its complex form can increase the sensitivity and specificity in the detection of activated brain regions both for event-related and block design paradigms when compared to magnitude-only applications. In addition, we introduce a novel fMRI phase-based visualization (FPV) technique to identify activated voxels such that the complex nature of the data is fully taken into account.