Reconstruction from incomplete data in cone-beam tomography

A method for reconstruction of an object f(x) x=(x,y,z) from a limited set of cone-beam projection data has been developed. This method uses a modified form of convolution back-projection and projection onto convex sets (POCS) for handling the limited (or incomplete) data problem. In cone-beam tomography, one needs to have a complete geometry to completely reconstruct the original three-dimensional object. While complete geometries do exist, they are of little use in practical implementations. The most common trajectory used in practical scanners is circular, which is incomplete. It is, however, possible to recover some of the information of the original signal f(x) based on a priori knowledge of the nature of f(x). If this knowledge can be posed in a convex set framework, then POCS can be utilized. In this report, we utilize this a priori knowledge as convex set constraints to reconstruct f(x) using POCS. While we demonstrate the effectiveness of our algorithm for circular trajectories, it is essentially geometry independent and will be useful in any limited-view cone-beam reconstruction.

Synthesis and characterization of a rare hemiacetalate bridged incomplete View the MathML source dicubane cluster

Reaction of 2-pyridinecarboxaldehyde [(Py)CHO] with Cu(NO3)2·2.5H2O in the presence of 4-aminopyridine and NaN3 in MeOH lead to an incomplete double-cubane [Cu4{PyCH(O)(OMe)}4(N3)4] (1) in 87% isolated yield, representing a rare type of metal cluster containing bridging hemiacetalate ligand [pyCH(O)(OMe)]−1 which was characterized by single crystal structure analysis and variable temperature magnetic behavior.

Incomplete decomposition of alkali metal azides

The thermal decomposition of sodium azide has been studied in the temperature range 240–360°C in vacuum and under pressure of an inert gas, argon. The results show that the decomposition is partial 360°C. From the observations made in the present work, namely: (i) the decomposition is incomplete both under vacuum and inert gas; (ii) mass spectrometric studies do not reveal any decrease in the intensity of the background species, CO+2, CO+, H2O+, and (iii) sodium metal remains in the ‘free state’ as seen by the formation of a metallic mirror at temperatures above 300°C, it has been argued that the partial nature of decompostion is due to the confinement of the decomposition to intermosaic regions within the lattice.

Chemistry of the incomplete decomposition of ammonium perchlorate (AP)

Results are presented to show that as the thermal decomposition of orthorhombic ammonium perchlorate proceeds there is an accumulation, in the solid, of hydrochloric and nitric acids, the concentrations of which increase up to 15% decomposition after which they decrease until they reach the original values.

Ruthenium-Oxygen Coordination-Driven Self-Assembly of a Ru-8(II) Incomplete Prism: Synthesis, Structure, and Shape-Selective Molecular Recognition Study

Coordination-driven self-assembly of 1,3,5-benzenetricarboxylate (tma; 1) and oxalato-bridged p-cymeneruthenium(II) building block Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (2) affords an unusual octanuclear incomplete prism Ru-8(eta(6)-p-cymene)(8)(tma)(2)(mu-eta(4)-C2O4)(2)(OMe)(4)](O3SCF3)( 2) (3), which exhibits a remarkable shape-selective binding affinity for neutral phenolic compounds via hydrogen-bonding interactions (p-cymene = p-(PrC6H4Me)-Pr-i). Such a binding was confirmed by single-crystal X-ray diffraction analysis using 1,3,5-trihydroxybenzene as an analyte.

Image reconstruction from incomplete projections data: A multiresolution modeling approach

Computerized tomography is an imaging technique which produces cross sectional map of an object from its line integrals. Image reconstruction algorithms require collection of line integrals covering the whole measurement range. However, in many practical situations part of projection data is inaccurately measured or not measured at all. In such incomplete projection data situations, conventional image reconstruction algorithms like the convolution back projection algorithm (CBP) and the Fourier reconstruction algorithm, assuming the projection data to be complete, produce degraded images. In this paper, a multiresolution multiscale modeling using the wavelet transform coefficients of projections is proposed for projection completion. The missing coefficients are then predicted based on these models at each scale followed by inverse wavelet transform to obtain the estimated projection data.

Enhanced photoabsorption efficiency of incomplete nanoshells

The rather low scattering or extinction efficiency of small nanoparticles, metallic and otherwise, is significantly enhanced when they are adsorbed on a larger core particle. But the photoabsorption by particles with varying surface area fractions on a larger core particle is found to be limited by saturation. It is found that the core-shell particle can have a lower absorption efficiency than a dielectric core with its surface partially nucleated with absorbing particles-an ``incomplete nanoshell'' particle. We have both numerically and experimentally studied the optical efficiencies of titania (TiO2) nucleated in various degrees on silica (SiO2) nanospheres. We show that optimal surface nucleation over cores of appropriate sizes and optical properties will have a direct impact on the applications exploiting the absorption and scattering properties of such composite particles.

Average Overlap for Clustering Incomplete Data using Symmetric Non-Negative Matrix Factorization

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

DSC studies on the phase transformation of hydrazonium sulfate

The high temperature phase transformation of hydrazonium sulfate, N2H6SO4 has been studied using DSC. The enthalpy of phase transition is found to be 3.63 ± 0.1 kJ mole−1. The phase transition temperature is found to decrease with the increase of particle size. It appears that the strain energy and not surface energy, is responsible for the phase transformation. The molar volume of the salt increases during the transformation as found by the dilatometric experiment involving percentage of linear thermal expansion. On cooling, the transformation from the high temperature modification to orthorhombic form is incomplete and extends over a wide range of temperature.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.