|Stochastic Systems Group|
Low SNR, Adaptive, Robust Non Gaussian Detection and Learning with application to fMRI data
Besides the signal component, measurments include noise that is non Gaussian in nature as well as interference components that reside in unkown subspace. Presence of both the noise and unknown interference components can significantly impact design and perforrmance of signal processing tasks such as detection of signal with signal subspace known as well as learning of signal subspace when signal subspacee is not known and needs to be estimated.
I intend to address the several novel facets of research in non Gaussian detection as well as learning. This research has been spurred by a real data driven need. Specifically need arose for functional MR where need to reduce false alarms became paramount without sacrificing enhanced sensitivity that obtains in presence of learning of response signature by exploiting spatio-temporal correlation in the data. The outcome of this effort led to the development of non Gaussian robust detection test. The presence of unknown interferents was addressed using min-max game thoeretic considerations. Additionally, Laplacian pdf was selected due to its "fat tail" characteristics to address "thin tail" related false alarms for Gaussian noise based detectors. Optimal Laplacian detector specifically developed for fmri yielded a generalization of t and F statistics associated with Gaussian noise Interestingly and importantly, the Laplacian detector was computationally implementable and the detector with adaptive learning of response singature ultimately produced superior results that avoided false alarms while presereving sensivity that usually accompanies learning.
Subsequently, the novel detection work has been extended to Generalized Gaussian family of pdfs which includes known pdfs such as Gaussain, Laplacian and uniform pdfs and then to a yet more broader family of log concave pdfs that includes pdfs associated with SIRP processes of interest in radar processing. Additionally, a spectrum of detectors also follow depending upon the approach taken to accommodate the prresence of unknonwn interfrence; and the spectrum of detecors lends readily to a hierachical mode of signal processing.
Besides detection, work has been expanded to subspace learning under non Gaussian noise, a problem made tractable for analysis due to a novel approach of looking subspaces that are least likley to explain the learning set of measurments. The results show specific forms of moment estimates of measurements that are needed for subspace learning. Specifically, it involves formation of second moment estimates of nonlinearly transformed measurements, and that solution involves solutionn of a nonlinear eigenvalue form of equation. Application of learning to Laplacian noise leads to an interesting result that subspace orientation is quantized. The facts that space is quantized lends to robustness of learning with respect to number of effects such as number of samples, noise, presence of interference effects.
If time permits I would briefly present ineteresting work in diffusion tensor MR data including challenges tensor nature of data presents in the processing of the data.
Work supported by NIH and Draper R&D funds.
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