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Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a…

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the absorption coefficient of the fluorophores at the excitation frequency and the quantum…

We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT)…

Bullet time is a type of visual effect commonly used in film, television and games that makes time seem to slow down or stop while still preserving dynamic details in the scene. It usually requires multiple sets of cameras to move slowly…

We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…

Dead time effects have been considered a major limitation for fast data acquisition in various time-correlated single photon counting applications, since a commonly adopted approach for dead time mitigation is to operate in the low-flux…

In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…

This paper examines the question of finding feasible points to discrete-time optimal control problems. The optimization problem of finding a feasible trajectory is transcribed to an unconstrained optimal control problem. An efficient…

The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary shaped lossy structures, such as those of…

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…

In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…

Near infrared diffuse optical tomography (DOT) provides an imaging modality for the oxygenation of tissue. In this paper, we propose a novel machine learning algorithm based on time-domain radiative transfer equation. We use temporal…

We present new results on an optical implementation of Grover's quantum search algorithm. This extends previous work in which the transverse spatial mode of a light beam oscillates between a broad initial input shape and a highly localized…

Imaging of rapidly occurring events in biology requires high temporal resolution. In this review article, I have tried to investigate an approximate estimate to quantify temporal resolution limit of a fluorescence imaging system. It was…

Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…

Time of flight cameras may emerge as the 3-D sensor of choice. Today, time of flight sensors use phase-based sampling, where the phase delay between emitted and received, high-frequency signals encodes distance. In this paper, we present a…

Fluorescence molecular tomography (FMT) is a sensitive optical imaging technology widely used in biomedical research. However, the ill-posedness of the inverse problem poses a huge challenge to FMT reconstruction. Although end-to-end deep…

A 3-D spatiotemporal prediction-error filter (PEF), is used to enhance foreground/background contrast in (real and simulated) sensor image sequences. Relative velocity is utilized to extract point-targets that would otherwise be…

Depth completion is crucial for many robotic tasks such as autonomous driving, 3-D reconstruction, and manipulation. Despite the significant progress, existing methods remain computationally intensive and often fail to meet the real-time…

Finite-difference time-domain (FDTD) is an effective algorithm for resolving Maxwell equations directly in time domain. Although FDTD has obtained sufficient development, there still exists some improvement space for it, such as…