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Many important microscopy samples, such as liquid crystals, biological tissue, or starches, are birefringent in nature. They scatter light differently depending on the light polarization and molecular orientations. The complete…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a…
This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…
In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneities…
This work proposes a green learning (GL) approach to restore medical images. Without loss of generality, we use low-dose computed tomography (LDCT) images as examples. LDCT images are susceptible to noise and artifacts, where the imaging…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Lensless cameras relax the design constraints of traditional cameras by shifting image formation from analog optics to digital post-processing. While new camera designs and applications can be enabled, lensless imaging is very sensitive to…
The biomechanical properties of cells and tissues play an important role in our fundamental understanding of the structures and functions of biological systems at both the cellular and subcellular levels. Recently, Brillouin microscopy,…
Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem is to reconstruct the source number, positions, and amplitudes. This problem arises from many important applications in…
Image relighting is the task of showing what a scene from a source image would look like if illuminated differently. Inverse graphics schemes recover an explicit representation of geometry and a set of chosen intrinsics, then relight with…
Ptychography is a lensless imaging technique, which considers reconstruction from a set of far-field diffraction patterns obtained by illuminating small overlapping regions of the specimen. In many cases, a distribution of light inside the…
Illumination estimation is often used in mixed reality to re-render a scene from another point of view, to change the color/texture of an object, or to insert a virtual object consistently lit into a real video or photograph. Specifically,…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Dual spectral computed tomography (DSCT) can achieve energy- and material-selective images, and has a superior distinguishability of some materials than conventional single spectral computed tomography (SSCT). However, the decomposition…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
This work is concerned with the problem of blind source separation and its applications to imaging. We first establish a theoretical result that we stated in our previous article on imaging in diffusive environments. This result is a…
Image light source transfer (LLST), as the most challenging task in the domain of image relighting, has attracted extensive attention in recent years. In the latest research, LLST is decomposed three sub-tasks: scene reconversion, shadow…