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The discrete Fourier transform is among the most routine tools used in high-resolution scanning / transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp…
Passive microrheology exploits the Brownian motion of colloidal tracer particles. From the mean-squared displacement (MSD) of the tracers, the bulk rheological and viscometric properties of the host medium can be inferred. Here, the MSD is…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…
Diffusion models can be used as learned priors for solving various inverse problems. However, most existing approaches are restricted to linear inverse problems, limiting their applicability to more general cases. In this paper, we build…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…
Reconstructing ghosting-free high dynamic range (HDR) images of dynamic scenes from a set of multi-exposure images is a challenging task, especially with large object motion and occlusions, leading to visible artifacts using existing…
Methods of three-dimensional deconvolution (3DD) or volumetric deconvolution of optical complex-valued wavefronts diffracted by 3D samples with the 3D point spread function are presented. Particularly, the quantitative correctness of the…
A direct sampling method (DSM) is designed herein for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the DSM is theoretically demonstrated by proving that…
Fourier ptychography microscopy (FPM), sharing its roots with synthetic aperture technique and phase retrieval method, is a recently developed computational microscopic super-resolution technique. By turning on the light-emitting diode…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
Owing to their tunability and versatility, the two-dimensional materials are an excellent platform to conduct a variety of experiments. However, laborious device fabrication procedures remain as a major experimental challenge. One…
Depth-from-Focus (DFF) enables precise depth estimation by analyzing focus cues across a stack of images captured at varying focal lengths. While recent learning-based approaches have advanced this field, they often struggle in complex…
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The…
While numerous optical methods exist to probe the dynamics of biological or complex fluid samples, in recent years digital Fourier microscopy techniques, like differential dynamic microscopy, have emerged as ways to efficiently combine…
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…
Dislocations control the mechanical behavior of crystalline materials, yet their quantitative characterization in bulk has remained elusive. Transmission Electron Microscopy provides atomic-scale resolution but is restricted to thin foils,…