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Thick biological tissues give rise to not only the scattering of incoming light waves, but also aberrations of the remaining unscattered waves. Due to the inability of existing optical imaging methodologies to overcome both of these…
Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
Specular reflections pose a significant challenge for object segmentation, as their sharp intensity transitions often mislead both conventional algorithms and deep learning based methods. However, as the specular reflection must lie on the…
Ring artifacts in computed tomography images, arising from the undesirable responses of detector units, significantly degrade image quality and diagnostic reliability. To address this challenge, we propose a dual-domain regularization model…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such…
We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
The translation of an early (1957), Russian article on the development of x-ray computed tomography is provided. The article demonstrates a principle possibility of determining the local attenuation coefficient in every element of a…
In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition…
Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…
Deep learning based image segmentation methods have achieved great success, even having human-level accuracy in some applications. However, due to the black box nature of deep learning, the best method may fail in some situations. Thus…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
The penetration power of x-rays allows one to image large objects. For example, centimeter-sized specimens can be imaged with micron-level resolution using synchrotron sources. In this case, however, the limited beam diameter and detector…
Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…