Related papers: Multiscale reverse-time-migration-type imaging usi…
Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system performance beyond the limit defined by its optical elements. The FPM technique applies a novel…
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lack translational symmetry or decay. In this paper, we…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
In this work, we propose a time-varying wave-shape extraction algorithm based on a modified version of the adaptive non-harmonic model for non-stationary signals. The model codifies the time-varying wave-shape information in the relative…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
This letter is focused on the design and analysis of computational wideband time-reversal imaging algorithms, designed to be adaptive with respect to the noise levels pertaining to the frequencies being employed for scene probing. These…
Seismic imaging faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Reverse time migration (RTM) is a high-resolution…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
We estimate the wave speed in the acoustic wave equation from boundary measurements by constructing a reduced-order model (ROM) matching discrete time-domain data. The state-variable representation of the ROM can be equivalently viewed as a…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We introduce a new modality for dynamic phase imaging in confocal microscopy based on synthetic optical holography. By temporal demultiplexing of the detector signal into a series of holograms, we record time-resolved phase images directly…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
In this paper we present a decomposition algorithm for computation of the spatial-temporal optical flow of a dynamic image sequence. We consider several applications, such as the extraction of temporal motion features and motion detection…