Related papers: Direct Sampling Method for Diffusive Optical Tomog…
We have developed a new technique called Direct Shear Mapping (DSM) to measure gravitational lensing shear directly from observations of a single background source. The technique assumes the velocity map of an un-lensed, stably-rotating…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are…
Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…
Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that…
We focus on coherent direction of arrival estimation of wideband sources based on spatial sparsity. This area of research is encountered in many applications such as passive radar, sonar, mining, and communication problems, in which an…
Limited-view artefacts are commonly present in optoacoustic tomography images, mainly due to practical geometrical and physical constraints imposed by the imaging systems as well as limited light penetration into large optically opaque…
When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…
Consider an operator equation (*) $B(u)+\ep u=0$ in a real Hilbert space, where $\ep>0$ is a small constant. The DSM (dynamical systems method) for solving equation (*) consists of a construction of a Cauchy problem, which has the following…
Diffuse optical tomography (DOT) is a severely ill-posed nonlinear inverse problem that seeks to estimate optical parameters from boundary measurements. In the Bayesian framework, the ill-posedness is diminished by incorporating {\em a…
A well-known diagnostic imaging modality, termed ultrasound tomography, was quickly developed for the detection of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation,…
We propose a novel approach for fast and accurate stereo visual Simultaneous Localization and Mapping (SLAM) independent of feature detection and matching. We extend monocular Direct Sparse Odometry (DSO) to a stereo system by optimizing…
Diffusion probabilistic models (DPMs) have achieved impressive success in visual generation. While, they suffer from slow inference speed due to iterative sampling. Employing fewer sampling steps is an intuitive solution, but this will also…
Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and…
Map matching for sparse trajectories is a fundamental problem for many trajectory-based applications, e.g., traffic scheduling and traffic flow analysis. Existing methods for map matching are generally based on Hidden Markov Model (HMM) or…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…
Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…
Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…
We present a detection scheme for diffusing wave spectroscopy (DWS) based on a two cell geometry that allows efficient ensemble averaging. This is achieved by putting a fast rotating diffuser in the optical path between laser and sample. We…