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An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…
The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
Effective clutter filtering is crucial in suppressing tissue clutter and extracting blood flow signal in Doppler ultrasound. Recent advances in eigen-based clutter filtering techniques have enabled ultrasound imaging of microvasculature…
Anomaly detection and localization in industrial images are essential for automated quality inspection. PaDiM, a prominent method, models the distribution of normal image features extracted by pre-trained Convolutional Neural Networks…
Currently, it is challenging to investigate aneurismal hemodynamics based on current in-vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment method, but can…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
In many places, tectonic tremor is observed in relation to slow slip and can be used as a proxy to study slow slip events of moderate magnitude where surface deformation is hidden in Global Navigation Satellite System (GNSS) noise. However,…
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Temporal anomaly detection looks for irregularities over space-time. Unsupervised temporal models employed thus far typically work on sequences of feature vectors, and much less on temporal multiway data. We focus our investigation on…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
Cardiovascular system study using ECG signals have evolved tremendously in the domain of electronics and signal processing. However, there are certain floating challenges unresolved in the analysis and detection of abnormal performances of…
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the…