Iterative Convolution Research Articles

Gravity analysis over the Aral, Black, and Caspian Seas from a combined GEOS 3/Seasat/Geosat altimeter data set

GEOS 3, Seasat and Geosat satellite altimetry data over the Aral, Black and Caspian Seas are processed using least squares collocation to predict geoid undulations and free‐air gravity anomalies on a 0.25° × 0.25° grid. A 180 × 180 geopotential model provides a reference surface for the collocation procedure and the framework for a regional map. Using local empirical covariance functions computed by an iterative numerical convolution technique, prediction accuracies of 24, 8, and 10 mGal were achieved for the Aral, Black, and Caspian Seas, respectively. Over the Caspian Sea, a hybrid theoretical/empirical covariance function was used to obtain reliable short‐wavelength gravity anomalies. The resulting regional gravity anomaly map confirms tectonic structures postulated by other investigators, reveals gravitational evidence of river sediments, and generally improves our knowledge of the geophysics of inland seas.

Halftoning with iterative convolution algorithm

We present a halftoning method based on iterative convolutions. In digital halftoning it is often useful to adapt the spectral properties of the halftoning algorithm to the local properties of the input image, e.g. its local grayvalue. In an iterative convolution algorithm this leads to the application of a space-variant impulse response in the halftoning process. Experiments demonstrate the properties and the control of this algorithm.

Volume estimates for log-concave densities with application to iterated convolutions

Volume estimates for log-concave densities with application to iterated convolutions

Configurational properties of charged hard sphere rings and stars in a solvent

The effect of charge and solvent density on the configurational properties of perfectly flexible hard sphere rings and stars is investigated on the basis of the iterative convolution approximation. It is found that solvent density has a negligible effect upon the configurational properties, while charge effects are substantial

Spatial inhomogeneities in emulsion polymerizations: repulsive wall calculations

The extent of the spatially inhomogeneous distribution of polymer particles in a latex formed by emulsion polymerization, dictated by thermodynamic considerations, is investigated computationally. Polymer chains suffer a loss of freedom near the particle surface, causing an entropic repulsion away from the surface and so favoring enhanced monomer concentration near the surface and thus polymerization by encapsulation. Thermodynamic calculations of the equilibrium polymer segment density distribution within a swollen latex particle show that while substantial entropic repulsions do occur, these are countered at higher polymer concentrations by polymer crowding effects. These calculations are performed using the iterative convolution technique to evaluate the segment-segment and segment-boundary correlations, corroborated where practicable with Monte Carlo calculations. This technique represents an advance over previous work which neglected polymer excluded-volume effects. Although the calculations were for low polymer fraction, trends from the results show that repulsive wall effects are highly unlikely to give rise to any significant inhomogeneities in latex particles formed from emulsion homopolymerization in conventional systems.

Deconvolution of disoriented fiber diffraction data using iterative convolution and local regression.

Computationally efficient procedures are described for the deconvolution of disoriented fiber diffraction data to the resolution limit of measurable intensity in the patterns. The methods can be applied to diffraction data from imperfectly parallel arrays of one-dimensionally periodic rods or two-dimensionally periodic sheets, randomly rotated about their unique axes, to derive a representation of the intensity distribution corresponding to perfectly parallel orientation. With use of angular convolution and local angular regression, a set of uniform cylindrically averaged squared structure factors are iteratively adjusted, subject to a minimum-wavelength constraint, until they produce a disoriented pattern that fits the observed diffraction data. The results from this deconvolution provide a measure of the properly scaled cylindrically averaged squared structure factors, which can be used with other structural information to construct a physically plausible trial model suitable for further refinement. Sample deconvolutions of simulated X-ray patterns from partially oriented gap junction membranes are presented and the results from point-model deconvolutions are compared to those from constrained deconvolutions that began with the transform of a physically plausible trial model.

Statistical theory of self-interacting elastomeric "star" networks: mechanical and scattering properties

The iterative convolution technique for the prediction of spatial correlation within polymeric systems is extended to the description of the structural and thermodynamic propertioes of athermal elastomeric networks. The role of excluded volume, the specification of crosslinkage and chain slipping at entanglements is investigated. The scattering functions from such networks are compared with experimental determinations and the qualitative agreement is found to be good

Iterative convolution determination of the mobility of knotted macromolcules

A statistical mechanical calculation of the mobility of a knotted macromolecule is presented on the basis of the iterative convolution approximation utilizing the Kirkwood-Riseman estimate of the translational friction coefficient. The linear relationship between mobility and the irreducible number of nodes or loops observed experimentally is confirmed. The magnitude of the diffusion coefficient appears to be a sensitive function of the excluded-volume processes operating within the entanglement, while the linear behavior derives from the specification of the central core of the knot from which the solvent is largely excluded

Application of Parallel Computing to the Monte Carlo Simulation of Electron Scattering in Solids: A Rapid Method for Profile Deconvolution

X-ray microanalysis by analytical electron microscopy (AEM) has proven to be a powerful tool for characterizing the spatial distribution of solute elements in materials. True compositional variations over spatial scales smaller than the actual resolution for microanalysis can be determined if the measured composition profile is deconvoluted. Explicit deconvolutions of such data, via conventional techniques such as Fourier transforms, are not possible due to statistical noise in AEM microanalytical data. Hence, the method of choice is to accomplish the deconvolution via iterative convolutions. In this method, a function describing the assumed true composition profile, calculated by physically permissible thermodynamic and kinetic modeling, is convoluted with the x-ray generation function and the result compared to the measured composition profile. If the measured and calculated profiles agree within experimental error, it is assumed that the true compositional profile has been determined. If the measured and calculated composition profiles are in disagreement, the assumptions in the physical model are adjusted and the convolution process repeated.

Rod-to-coil and order-disorder transitions in nematic polymers

The nematic order parameter S of a linear, semiflexibly linked sequence of rigid rods is determined with respect to an external director field as a function of length, reduced temperature, and chain stiffness on the basis of the iterative convolution approximation. The mean-square length and the mean-square radius of gyration are also determined as a function of these parameters. It is found that all systems exhibit a pronounced order-disorder transition over a narrow range of reduced temperature, although this does not necessarily imply a rod-coil transition

Solving the attenuation problem in emission computed tomography using homomorphic filters

An approach to the attenuation problem in positron emission computed tomography (PET) is discussed. The underlying idea of the method, in which a homomorphic system and an iterative convolution backprojection algorithm are employed, is described. The use of these two algorithms in the new algorithm is discussed. Results obtained with the algorithms are judged acceptable, with the reconstructed images of many different phantoms tested seeming to converge after several iterations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Photoluminescence lifetime microscope spectrometer based on time-correlated single-photon counting with an avalanche diode detector

A photoluminescence lifetime microscope spectrometer (PLμS) based on time-correlated single-photon counting (TCSPC) with a single-photon avalanche diode (SPAD) detector was developed for the investigation of the microscopic spatial fluctuations of the minority-carrier lifetime and other material parameters in gallium arsenide (GaAs) and related compound semiconductors. The high sensitivity of the TCSPC technique is essential for time-resolved photoluminescence (TRPL) measurements with a spatial resolution of the order of a few micrometers. The spatial resolution of the PLμS is compatible with the diffusion length in GaAs substrates or the dimensions of small, highly integrated GaAs devices. The PLμS is the first instrument of its kind based entirely on solid-state components, i.e., a gain-switched diode laser for pulsed excitation and an avalanche diode for single-photon detection. It is explained why, in samples dominated by nonradiative linear recombination, the relatively large excitation pulse width of the diode laser compared to a synchronously pumped dye laser does not adversely affect the timing accuracy of the measured decay time constants. It was previously shown that, by using nonlinear least-squares iterative convolution analysis, a TCSPC instrument with an instrumental response width of 70 ps (FWHM) is capable of accurately measuring fluorescence decay time constants down to 10 ps with ±2 ps timing accuracy. The PLμS is designed to take full advantage of the high repetition rates, up to 100 MHz, typical for mode-locked laser sources or gain-switched diode lasers. The data-acquisition time for a complete decay curve containing typically several hundred thousand counts is thus reduced to a few seconds. Hence, the PLμS is, in principle, suitable for scanning operation and topographical imaging.

Consistent iterative convolution: a coupled approach to tomographic reconstruction

Iterative convolution, a technique for limited-data tomographic reconstruction, is based on constrained iteration between a source function’s estimated image and its Radon transform. For certain source functions, the estimated image diverges from the source function. This divergence is shown to result from the algorithm’s failure to enforce consistency between the estimated image and its measured Radon transform. To correct for this, consistency can be enforced by using a routine based on the direct-inversion formula and on decomposing the image into components generated from its measured and missing Radon-transform integrals. This routine was used to develop a new iterative scheme that converges absolutely for three test objects for which simple iterative convolution diverges.

Characteristics of the pulmonary transport functions for heat and dye in pulmonary edema and orthostasis.

The aim of this study was to investigate whether changes in the distribution of pulmonary blood flow and disturbances of the pulmonary microcirculation can be detected by use of inflow-outflow indicator-dilution measurements. In 18 anesthetized (N2O-piritramide) mongrel dogs 221 thermal-indocyanine green dye indicator dilution kinetics were recorded in the pulmonary artery and aorta after central venous indicator injection. The lagged normal density function was used as a model for the pulmonary transport functions for heat and dye. The parameters of the lagged normal density function were computed by a non-linear least squares procedure by iterative convolution. After baseline measurements, in nine dogs, pulmonary edema was induced by central venous application of oleic acid. In nine other dogs, measurements were performed before and after postural changes. Our data show that both the microvascular injury caused by oleic acid edema and the perfusion heterogeneity caused by orthostasis can be detected by the indicator dilution technique since the both relative dispersion and skewness of the transport functions for heat and dye were significantly increased after these interventions.

Conical bores. Part II: Multiconvolution

The input impulse response, or related functions such as the plane-wave or spherical-wave reflection functions, of a conical bore with discontinuities can be calculated from the reflection functions associated with discontinuities by means of a multiconvolution process. This approach, as alternative to the Fourier transform of the acoustical impedance Z(f), is attractive because of the detailed description it gives of the pressure time evolution inside the bore. However, the calculation may become rather involved if each reflected and transmitted wave is followed individually, and numerical instability may arise whenever the implied reflection functions contain growing exponentials. The first difficulty has been overcome by summing up all outward traveling waves and all inward traveling waves to give a unique outward wave and a unique inward wave. Numerical instability has been avoided by using an iterative convolution algorithm. Internal damping due to viscous and thermal losses has been located at discontinuities and represented by means of damping functions through convolution products. The reflection functions used are presented in the companion article ‘‘Conical bores. Part I: Reflection functions associated with discontinuities’’ [Martínez and Agulló, J. Acoust. Soc. Am. 84, 1613–1619 (1988)].

Iterative convolution calculations of particle scattering functions for self-avoiding polymer systems

Iterative convolution calculations of particle scattering functions for self-avoiding polymer systems

Role of excluded volume in the configurational properties of uniform star polymers; iterative convolution and Monte Carlo simulation

Role of excluded volume in the configurational properties of uniform star polymers; iterative convolution and Monte Carlo simulation

Design Methods for Cascaded Gaussian Filters

AbstractThis paper considers the multiresolution (in terms of standard deviation) Gaussian filter, which plays an important role in the visual information processing and the signal analysis. A high‐speed and highly accurate method is proposed for Gaussian filtering and calculation of its derivative, using the filter with a recursive structure utilizing the properties of Gaussian function. The earlier method, based on the iterative convolution of Gaussian function, is generalized. The problem is reformulated permitting the variation of the weight coefficient and the scale factor (expansion ratio of standard deviation), to achieve a sufficient accuracy. First, a formulation is made for the continuous system to realize a Gaussian filter and the sequence of its derivative filters for the specified scale factor. Then based on the result, a generation formula is derived for the filter sequence in the discrete system by iterative convolutions with the same weight coefficient. Furthermore, the factors for the error in discrete representation is analyzed, and the condition is derived for suppressing the error.

Site-selective fluorescence and hole-burning spectroscopy of MTHF glasses doped with tetracene or pentacene

Site-selective fluorescence spectra of tetracene (TC) doped in a MTHF glass have been recorded as a function of excitation energy. Based upon the true inhomogeneous absorption profile of the TC S 1 ← S 0 origin determined via vibrational ZP emission intensities the true phonon wing has been evaluated employing an iterative numerical spectral convolution procedure. It is found that both phonon spectra and Debye-Waller factor are virtually constant (α = 0.55 ± 0.08) across the inhomogeneous absorption band as are hole-burning yields in MTHF:TC glasses if probed in the zero-phonon line fluorescence excitation mode. It is concluded that the distributions of both the rate constant for NPHB and the strength of electron-phonon coupling are uncorrelated with the electronic site excitation energies.

A Monte Carlo analysis of terminally attached self-avoiding polymer sequences in the vicinity of a rigid boundary

A Monte Carlo analysis of terminally attached hard sphere sequences of N<or=24 segments in the vicinity of a rigid plane is presented. The principal configurational properties of the system are determined, in particular the segment density distribution rho (z mod N) normal to the boundary, the mean square end-to-end length (R1N2), the mean square radius of gyration (SN2) and the mean thickness of the adsorbed layer (z1N). Comparisons with a previously presented iterative convolution analysis are made and the existence of a density discontinuity in rho (z mod N) is confirmed. Exponent representation of the data suggest (R1N2) approximately (N-1)gamma with gamma approximately 1.2, consistent with lattice-based analyses. The boundary configurations are resolved into loop, train and tail components and their dependence upon chain length determined. Good agreement with the convolution analysis is found, the results being consistent with earlier analyses by Roe (1965) and Chan et al. (1975), and the experimental investigations of Cosgrove et al. (1983).