Related papers: Tomographic Reconstruction Methods for Decomposing…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, information from previous longitudinal scans of the same…
We consider the problem of atmospheric tomography, as it appears for example in adaptive optics systems for extremely large telescopes. We derive a frame decomposition, i.e., a decomposition in terms of a frame, of the underlying…
We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the…
Recovering 3D geometry and textures of individual objects is crucial for many robotics applications, such as manipulation, pose estimation, and autonomous driving. However, decomposing a target object from a complex background is…
We use a spatial light modulator in a diffraction tomographic system to assess the accuracy of different refractive index reconstruction algorithms. Optical phase conjugation principles through complex media, allows us to quantify the error…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views…
We develop a cylindrical shape decomposition (CSD) algorithm to decompose an object, a union of several tubular structures, into its semantic components. We decompose the object using its curve skeleton and restricted translational sweeps.…
We present a technique for a complete 3D reconstruction of small objects moving in front of a textured background. It is a particular variation of multibody structure from motion, which specializes to two objects only. The scene is captured…
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…
In this review we present an overview of the current atom probe tomography spatial data reconstruction paradigm, and explore some of potential routes to improve the current methodology in order to yield a more accurate representation of…
Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…
We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The…