Direct Reconstruction Method Research Articles

Quantitative palaeobiogeography: GIS, phylogenetic biogeographical analysis, and conservation insights

AbstractAim The utility of GIS‐based and phylogenetic biogeographical analysis in palaeobiogeography is reviewed with reference to its ability to elucidate patterns of interest for modern conservation biology, specifically the long‐term effects of invasive species.Location Emphasis is on biogeographical patterns in the Appalachian basin and mid‐continent of North America during the Devonian. Global palaeobiogeographical patterns of the Cambrian are also considered.Methods Palaeobiogeographical patterns are assessed within a GIS framework, including both direct range reconstruction and niche modelling methods, and within phylogenetic biogeographical analysis. Biogeographical patterns are considered within multiple clades of fossil invertebrates, including trilobites, crustaceans, brachiopods, and bivalves.Results GIS‐based analysis (including niche modelling methods) of Devonian invertebrates demonstrates a tightly correlated relationship between sea‐level rises and range expansion, dispersal events, and species invasions. The predominance of range expansion and species invasions during the Late Devonian reduced opportunities for vicariant speciation during this interval. Comparison of phylogenetic biogeographical patterns between Cambrian and Devonian trilobites allows discernment of the relative roles of tectonics and eustacy in driving biogeographical patterns.Main conclusions GIS analysis and phylogenetic biogeography are powerful tools for analysing the coevolution of the Earth and its biota. Analyses can identify episodes of vicariance and geo‐dispersal and produce testable hypotheses for further analysis within the fossil record.

Improving Non-Cartesian MRI Reconstruction through Discontinuity Subtraction

Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). Accurate and fast image reconstruction from non-Cartesian k-space data becomes a challenge and gains a lot of attention. Images provided by conventional direct reconstruction methods usually bear ringing, streaking, and other leakage artifacts caused by discontinuous structures. In this paper, we tackle these problems by analyzing the principal point spread function (PSF) of non-Cartesian reconstruction and propose a leakage reduction reconstruction scheme based on discontinuity subtraction. Data fidelity in k-space is enforced during each iteration. Multidimensional nonuniform fast Fourier transform (NUFFT) algorithms are utilized to simulate the k-space samples as well as to reconstruct images. The proposed method is compared to the direct reconstruction method on computer-simulated phantoms and physical scans. Non-Cartesian sampling trajectories including 2D spiral, 2D and 3D radial trajectories are studied. The proposed method is found useful on reducing artifacts due to high image discontinuities. It also improves the quality of images reconstructed from undersampled data.

A flexible and robust direct reconstruction method for magnetospheric radio tomography

We present a flexible and robust direct reconstruction method for magnetospheric radio tomography. We show that for a combined reconstruction of plasma density Ne and magnetic field B, the direct reconstruction method performs as well as popular iterative methods such as algebraic reconstruction technique (ART) and multiplicative algebraic reconstruction technique (MART) for large number of satellites, but it performs significantly better when the number of satellites is small. The main advantages of this method are that extra information, such as in situ measurements, can be easily and flexibly incorporated into the reconstruction; it is relatively robust in the presence of noise; and it is less sensitive than other methods to numerical reconstruction parameters like assumed grid size. We demonstrate the good performance of this method in reconstructing electron density and magnetic field using constellations of relatively few satellites (11 and fewer) in a single orbit in a variety of magnetospheric regions. Although this method is relatively robust to noisy measurements, local measurements can significantly increase the reconstruction accuracy.

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

A direct reconstruction method with variable constraints

In this article. a direct method to reconstruct images from projections is presented. This method, having its origin in astrophysics to restore images from observed data, uses a constant upper bound and a variable lower bound to constrain the maximum and minimum values taken by the emission intensity during iteration. Computer-simulated emission projection data from two phantoms are used for reconstruction. Comparison is made with other methods. The results show that a much better spatial resolution can be acquired by this method, especially for the sharp-shaped emission sources. (C) 1999 John Wiley & Sons, Inc.

A direct reconstruction method with variable constraints

A direct reconstruction method with variable constraints

Kalman sinogram restoration for fast and accurate PET image reconstruction

Sinogram restoration followed by filtered backprojection has been shown to be a fast alternative to direct image reconstruction method for obtaining PET images of good quality and quantitative accuracy. In previous studies, the authors used detector motion and the method of projection onto convex sets for sinogram restoration; but, the performance was observed to degrade rapidly when the noise level of PET data increased. In this paper, the authors describe a sinogram restoration method based on Kalman filtering that provides surprisingly good results with very fast computations. The new method shows greatly improved noise performance at realistic noise levels, and its computational cost is little more than that of conventional PET image reconstruction by filtered backprojection.

Measurement of the W boson mass from direct reconstruction at LEP

The measurement of the mass of the W boson with the direct reconstruction method is described. Preliminary results obtained by the four LEP experiments with the data collected in 1996 at √ s = 170−172 GeV are presented.

Perturbative rates and colour rearrangement effects in four-jet events at LEP2

An important issue in the direct reconstruction method of determining the $W$ mass from $q\bar q Q\bar Q$ events at LEP2 concerns the impact of the relatively unknown QCD interconnection effects. It has been suggested that a study of `short string' states, in which colour singlet states are formed from $q \bar Q $ and $Q\bar q$ pairs with small phase--space separation, could shed important light on this issue. We show that such configurations can also be generated by conventional background $e^+e^-\ar 4$~parton processes, in particular QCD $q \bar q g g$ and $q \bar q Q \bar Q$ and non--resonant electroweak $q \bar q Q \bar Q$ production. We study the colour and kinematic structure of these background contributions, and estimate the event rate to be expected at LEP2. We find that the QCD processes are heavily suppressed, but that non--resonant $q \bar q Q \bar Q$ production may be comparable in rate to the expected `short string' signal from $W^+W^-$ production.

Direct reconstruction method for wavelet transform extrema representation

In contrast to the iterative reconstruction algorithm of projections onto convex sets (Mallat and coworkers, 1992; Liew and Nguyen, 1995; Cvetkovic and Vetterli, 1995) a noniterative method that completely solves the problem of reconstructing from the wavelet transform extrema representation is presented for the first time. The solution obtained by the proposed method is mathematically consistent and is indistinguishable from the true solution, i.e. both give the same representation. The proposed method consists of first finding a least-squares solution in the space spanned by the wavelet sampling bases. An orthogonal component that is to be added to the least-squares solution to form a consistent solution is then found by solving a set of linear inequalities specified by the a priori information in the representation using the linear programming technique. Numerical results presented show that the reconstructions are of good quality.

Unbiased Cluster Lens Reconstruction

Weak lensing observations measure the shear field and hence the gradient of the dimensionless surface density $\kappa$. We present several new algorithms to recover $\kappa$ {}from shear estimates on a finite region and compare how they perform with realistically noisy data. The reconstruction methods studied here are divided into 2 classes: direct reconstruction and regularized inversion. Direct reconstruction techniques express $\kappa$ as a 2D integral of the shear field. This yields an estimator for $\kappa$ as a discrete sum over background galaxy ellipticities which is straightforward to implement, and allows a simple estimate of the noise. We study 3 types of direct reconstruction methods: 1) $\kappa$-estimators that measure the surface density at any given target point relative to the mean value in a reference region 2) a method that explicitly attempts to minimize the rotational part of $\nabla \kappa$ that is due to noise and 3) a novel, exact Fourier-space inverse gradient operator. We also develop two `regularized maximum likelihood' methods, one of which employs the conventional discrete Laplacian operator as a regularizer and the other uses regularization of all components in Fourier space. We compare the performance of all the estimators by means of simulations and noise power analysis. A general feature of these unbiased methods is an enhancement of the low frequency power which, for some of the methods, can be quite severe. We find the best performance is provided by the maximum likelihood method with Fourier space regularization although some of the other methods perform almost as well.

An alternative approach to direct Fourier reconstruction in parallel-beam tomography

In this work, we elaborate on some of the features of the direct Fourier reconstruction method, which has not spurred much interest in the literature. We searched for the possibility of an interpolation in the object space prior to Fourier transformation of the projection. To implement this idea, the central slice theorem based on the finite Fourier transform is reconsidered for a density distribution of point weights placed over a square grid. Some industrial applications carried out on a scanner with a Cs-137 source are given to demonstrate and verify our algorithm. It is observed that the image resolution is improved over that obtainable by the application of the basic direct Fourier transform method.

Direct reconstruction methods for hyperspectral imaging with rotational spectrotomography

A new technique for hyperspectral imaging called spectrotomography collects all available photons and relies on computer tomography to reconstruct the three-dimensional data cube of an object. A rotational spectrotomographic (RST) imager is designed with a wide-aperture, objective-grating camera that is rotated in steps around its optical axis. The full range of spatial and spectral resolution is achieved by the use of a stepped-focal-length (zoom) lens to illuminate the grating. Two-dimensional projections of the object are analyzed with the use of both direct Fourier methods and filter-backprojection algorithms. The RST imager has applications to detection of optical emissions where large photon throughput is required.

Impedance tomography: computational analysis based on finite element models of a cylinder and a human thorax.

A direct image reconstruction method of electrical impedance tomography (EIT) is evaluated using three-dimensional (3-D) finite element models of cylindrical and torso-shaped volume conductors. The cylindrical model is used to examine the effect of electrode configurations and the sensitivity to off-plane objects and to noise in the measured data. It is also used to validate the modeling procedures by comparison with experimental data acquired from a similar cylindrical tank filled with saline. Simulation results show only minor differences in performance between the various electrode configurations. In the second part, a realistic human thorax model constructed from CT images is used to evaluate monitoring of pulmonary edema by EIT. The conductivity, volume, and vertical position of an abnormal region in the lungs are varied to simulate the progress of edema. Dynamic EIT images are reconstructed from data computed for the inhomogeneous thorax (heart and lungs) as the reference set and a realistic amount of noise is added to reproduce the conditions in which the technique would be used in practice. Simulation results show that a 10 ml edema region with a conductivity equal to that of blood can be detected at a 40 dB signal-to-noise ratio (SNR). Detection of a smaller volume, in the order of 2 ml, should be possible by improving either the instrumentation to achieve 60 dB SNR or the performance of reconstruction algorithms.

Computer analysis of side-band holography in STEM

The feasibility of a recently proposed method for direct reconstruction of a wave function at the exit plane of an object is tested on the basis of computer simulation. It is assumed that the point electron source of a STEM instrument is ideally coherent. Optimum imaging conditions for recording of a hologram are found with respect to a restoration error as a function of the desired spatial resolution of a restored wave function and the accelerating voltage. The highest spatial resolution that can be achieved for 100 and 300 kV holography is determined. The size of a region is determined for which the wave function can be restored for any one beam position. Accuracy requirements to which the experimental imaging conditions should be known are worked out.

Direct recording and reconstruction of 3-D x-ray images

Theoretical and experimental investigations of a method for direct recording and reconstruction of 3-D x-ray images are described. When recording, an x-ray source is placed at discrete positions, and an x-ray grid is fixed on the x-ray plate. When reconstructing, a lenticular sheet matched with the grid is overlayed on the developed plate, and a parallax-panoramagram type 3-D image is seen with the naked eye. Using a small x-ray source designed for use in dental clinics and an x-ray grid matched with the lenticular sheet, 3-D x-ray images having a 0.001-rad resolvable angle and a 0.02-rad flipping angle are directly recognized with clear parallax.

Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography

We give a new method for direct reconstruction of three-dimensional objects from a few electron micrographs taken at angles which need not exceed a range of 60 degrees. The method works for totally asymmetric objects, and requires little computer time or storage. It is also applicable to X-ray photography, and may greatly reduce the exposure compared to current methods of body-section radiography.