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Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
This paper introduces a new approach to patch-based image restoration based on external datasets and importance sampling. The Minimum Mean Squared Error (MMSE) estimate of the image patches, the computation of which requires solving a…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final…
Semantic segmentation benchmarks in the realm of autonomous driving are dominated by large pre-trained transformers, yet their widespread adoption is impeded by substantial computational costs and prolonged training durations. To lift this…
Electroencephalogram (EEG) recordings are often contaminated with artifacts. Various methods have been developed to eliminate or weaken the influence of artifacts. However, most of them rely on prior experience for analysis. Here, we…
We present a transformer-based image anomaly detection and localization network. Our proposed model is a combination of a reconstruction-based approach and patch embedding. The use of transformer networks helps to preserve the spatial…
Seismic signal is used for vehicle classification widely. However, this task becomes difficult as a result of various noises. To solve the problem, this paper proposes a novel de-noising algorithm which evolves from a nonparametric adaptive…
This paper investigates the problem of sampling and reconstructing bandpass signals using time encoding machine(TEM). It is shown that the sampling in principle is equivalent to periodic non-uniform sampling (PNS). Then the TEM parameters…
This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate the instantaneous information of well-separated modes…
Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential…
An applied problem facing all areas of data science is harmonizing data sources. Joining data from multiple origins with unmapped and only partially overlapping features is a prerequisite to developing and testing robust, generalizable…
Amplitude demodulation is a classical operation used in signal processing. For a long time, its effective applications in practice have been limited to narrowband signals. In this work, we generalize amplitude demodulation to wideband…
Image compression constitutes a significant challenge amidst the era of information explosion. Recent studies employing deep learning methods have demonstrated the superior performance of learning-based image compression methods over…
In this study, the Multivariate Empirical Mode Decomposition (MEMD) approach is applied to extract features from multi-channel EEG signals for mental state classification. MEMD is a data-adaptive analysis approach which is suitable…
Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…
In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
The characterization of multicomponent signals with a particular emphasis on musical and communication signals is one of the problems studied in the dissertation. In order to provide an efficient analysis of the multicomponent signals, the…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…