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Functional Magnetic Resonance Imaging (fMRI) is an advanced neuroimaging method that enables in-depth analysis of brain activity by measuring dynamic changes in the blood oxygenation level-dependent (BOLD) signals. However, the…
In order to support diverse scenarios and deployments, the numerology of orthogonal frequency division multiplexing (OFDM) is defined for the parametrization of subcarrier spacing and cyclic prefix (CP). The time-frequency dispersion of…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…
We present an approach for the detection of sharp change points (short-lived and persistent) in nonlinear and nonstationary dynamic systems under high levels of noise by tracking the local phase and amplitude synchronization among the…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Intrinsic image decomposition is an important and long-standing computer vision problem. Given an input image, recovering the physical scene properties is ill-posed. Several physically motivated priors have been used to restrict the…
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…
This thesis delves into the world of non-invasive electrophysiological brain signals like electroencephalography (EEG) and magnetoencephalography (MEG), focusing on modelling and decoding such data. The research aims to investigate what…
Dynamical modeling of multisite human intracranial neural recordings is essential for developing neurotechnologies such as brain-computer interfaces (BCIs). Linear dynamical models are widely used for this purpose due to their…
This paper addresses the problem of multi-channel multi-speech separation based on deep learning techniques. In the short time Fourier transform domain, we propose an end-to-end narrow-band network that directly takes as input the…
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a…
During recent years, dynamical decoupling (DD) has gained relevance as a tool for manipulating quantum systems and extracting information from them. This is particularly relevant for spins involved in nuclear magnetic resonance (NMR), where…
Out-of-distribution detection is crucial to the safe deployment of machine learning systems. Currently, unsupervised out-of-distribution detection is dominated by generative-based approaches that make use of estimates of the likelihood or…
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…
Dynamic functional connectivity (DFC) analysis involves measuring correlated neural activity over time across multiple brain regions. Significant regional correlations among neural signals, such as those obtained from resting-state…
Recently, the potential of dynamic brain networks as a neuroimaging biomarkers for mental illnesses is being increasingly recognized. However, there are several unmet challenges in developing such biomarkers, including the need for methods…
Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…