Exact Reconstruction Method Research Articles

Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method

We derive the extension of the classical d’Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index. Analogous formulae exist already in the literature, but in the current work this is derived in a natural way for general incident field, by employing results obtained via the Fokas method. This methodology is further extended to a medium with piecewise constant refractive index, providing the apparatus for the solution of the associated inverse scattering problem. Hence, we provide an exact reconstruction method which is also valid for phaseless data.

An analytic method for the inverse problem of MREPT

Magnetic resonance electric properties tomography (MREPT) is a medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. This method consists of reconstructing the admittivity distribution from the positive rotating component of the magnetic field. In the newest paper of Ammari et al (2015 Inverse Problems 31 105001) an approximate method of reconstruction of variable admittivity was proposed. In this paper a method for exact reconstruction of the admittivity from data of the positive rotating component of the field is given.

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstruction procedure that can provide the foundation for an efficient algorithm. For a broad class of functions, including piecewise polynomials and generalized splines, we prove that an exact reconstruction is possible by minimizing a generalized total variation seminorm along lines. The main difference with previous works is that our approach is inherently one-dimensional and that it imposes less constraints on the class of admissible signals. Within this formulation, we derive unique reconstruction results using properties of the Hilbert transform, and we present numerical examples of the reconstruction.

Exact reconstruction method for on-machine measurement of profile

We present a new reconstruction method for measuring profile of large, ultraprecise absolute optical surfaces with a compact interferometer. The profile of workpiece can be reconstructed exactly with high lateral resolution and large non-equidistant scanning step. Both systematic errors of the interferometer and height offsets of the scanning stage can be eliminated. Additional angular measurement can be used to measure pitching angles of the scanning stage. The exact reconstruction method is verified by computer simulation and on-machine measurement experiment.

Whole-Body Cerenkov Luminescence Tomography with the Finite Element SP3 Method

Generation of an accurate Cerenkov luminescence imaging model is a current issue of nuclear tomography with optical techniques. The article takes a pro-active approach toward whole-body Cerenkov luminescence tomography. The finite element framework employs the equation of radiative transfer via the third-order simplified spherical harmonics approximation to model Cerenkov photon propagation in a small animal. After this forward model is performed on a digital mouse with optical property heterogeneity and compared with the Monte Carlo method, we investigated the whole body reconstruction algorithm along a regularization path via coordinate descent. The endpoint of the follow-up study is the in vivo application, which provides three-dimensional biodistribution of the radiotracer uptake in the mouse from measured partial boundary currents. The combination of the forward and inverse model with elastic-net penalties is not only validated by numerical simulation, but it also effectively demonstrates in vivo imaging in small animals. Our exact reconstruction method enables optical molecular imaging to best utilize Cerenkov radiation emission from the decay of medical isotopes in tissues.

Cone‐Beam Composite‐Circling Scan and Exact Image Reconstruction for a Quasi‐Short Object

Here we propose a cone-beam composite-circling mode to solve the quasi-short object problem, which is to reconstruct a short portion of a long object from longitudinally truncated cone-beam data involving the short object. In contrast to the saddle curve cone-beam scanning, the proposed scanning mode requires that the X-ray focal spot undergoes a circular motion in a plane facing the short object, while the X-ray source is rotated in the gantry main plane. Because of the symmetry of the proposed mechanical rotations and the compatibility with the physiological conditions, this new mode has significant advantages over the saddle curve from perspectives of both engineering implementation and clinical applications. As a feasibility study, a backprojection filtration (BPF) algorithm is developed to reconstruct images from data collected along a composite-circling trajectory. The initial simulation results demonstrate the correctness of the proposed exact reconstruction method and the merits of the proposed mode.

Changes in anthropometrical data of the Hungarian child and adult population during the last thirty years based on family studies conducted by the Department of Forensic Medicine at Budapest

Studies of the Hungarian child and adult population have revealed striking changes over the past thirty years with respect to body height and body mass, an observation, which has also been confirmed by other investigations (Gyenis & Joubert 2003, Maródi et. al. 2002). Based on these deviations the authors were interested in the variability of some anthropometrical head measures, which are of particular importance for forensic anthropological questions concerning face reconstruction (Editorial 2001, Jayprakash et. al. 2001, Szilvdssy & Kritscher 1997, Szilvdssy et al. 1997). The majority of such reconstruction methods, however, do not take into consideration the process of secular trend. It is the aim of this study to improve the anthropological basis for exact reconstruction methods by elaboration of temporal changes of face, head and body measures of the Hungarian population collected during the past thirty years. For this data from 2353 adults and 861 children investigated in 1974, and 869 adults 287 children investigated between 1994 and 2004 are available.

Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data.

The n-PI-method for helical cone-beam CT.

A new class of acquisition schemes for helical cone-beam computed tomography (CB-CT) scanning is introduced, and their effect on the reconstruction methods is analyzed. These acquisition schemes are based on a new detector shape that is bounded by the helix. It will be shown that the data acquired with these schemes are compatible with exact reconstruction methods, and the adaptation of exact reconstruction algorithms to the new acquisition geometry is described. At the same time, the so-called PI-sufficiency condition is fulfilled. Moreover, a good fit to the acquisition requirements of the various medical applications of cone-beam CT is achieved. In contrast to other helical cone-beam acquisition and reconstruction methods, the n-PI-method introduced in this publication allows for variable pitches of the acquisition helix. This additional feature will introduce a higher flexibility into the acquisition protocols of future medical cone-beam scanners. An approximative n-PI-filtered backprojection (n-PI-FBP) reconstruction method is presented and verified. It yields convincing image quality.