In this paper, we introduce a likelihood model for tracking the location of object in multiple view systems. Our proposed model transforms conventional nonlinear Euclidean estimation model to an estimation model based on the manifold tangent subspace. In this paper, we show that by decomposition of input noise into two parts and description of model by exponential map, real observations in the Euclidean geometry can be transformed to the manifold tangent subspace. Moreover, by obtained tangent subspace likelihood function, we propose two iterative and noniterative maximum likelihood estimation approaches which numerical results show their good performance.
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http://dx.doi.org/10.1109/TCYB.2016.2624309 | DOI Listing |
Med Biol Eng Comput
June 2024
Department of Biomedical Engineering, University of Houston, Houston, TX, 77204, USA.
Motor imagery (MI) paradigms have been widely used in neural rehabilitation and drowsiness state assessment. The progress in brain-computer interface (BCI) technology has emphasized the importance of accurately and efficiently detecting motor imagery intentions from electroencephalogram (EEG). Despite the recent breakthroughs made in developing EEG-based algorithms for decoding MI, the accuracy and efficiency of these models remain limited by technical challenges posed by cross-subject heterogeneity in EEG data processing and the scarcity of EEG data for training.
View Article and Find Full Text PDFJ Math Biol
July 2023
Department of Mechanical Engineering, Khalifa University of Science and Technology, 127788, Abu Dhabi, UAE.
We present "on the fly" algorithmic criteria for the accuracy and stability (non-stiffness) of reduced models constructed with the quasi-steady state and partial equilibrium approximations. The criteria comprise those introduced in Goussis (Combust Theor Model 16:869-926, 2012) that addressed the case where each fast time scale is due to one reaction and a new one that addresses the case where a fast time scale is due to more than one reactions. The development of these criteria is based on the ability to approximate accurately the fast and slow subspaces of the tangent space.
View Article and Find Full Text PDFChaos
June 2023
Kotelnikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russia.
We present a modified complex-valued Shimizu-Morioka system with a uniformly hyperbolic attractor. We show that the numerically observed attractor in the Poincaré cross section expands three times in the angular direction and strongly contracts in the transversal directions, similar in structure to the Smale-Williams solenoid. This is the first example of a modification of a system with a genuine Lorenz attractor, but manifesting a uniformly hyperbolic attractor instead.
View Article and Find Full Text PDFMagn Reson Med
April 2023
Gordon Center for Medical Imaging, Department of Radiology, Massachusetts General Hospital, Boston, Massachusetts, USA.
Purpose: To develop a manifold learning-based method that leverages the intrinsic low-dimensional structure of MR Spectroscopic Imaging (MRSI) signals for joint spectral quantification.
Methods: A linear tangent space alignment (LTSA) model was proposed to represent MRSI signals. In the proposed model, the signals of each metabolite were represented using a subspace model and the local coordinates of the subspaces were aligned to the global coordinates of the underlying low-dimensional manifold via linear transform.
The spatial resolution and temporal frame-rate of dynamic magnetic resonance imaging (MRI) can be improved by reconstructing images from sparsely sampled k -space data with mathematical modeling of the underlying spatiotemporal signals. These models include sparsity models, linear subspace models, and non-linear manifold models. This work presents a novel linear tangent space alignment (LTSA) model-based framework that exploits the intrinsic low-dimensional manifold structure of dynamic images for accelerated dynamic MRI.
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