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.

Application of regularization methods to damage detection in large scale plane frame structures using incomplete noisy modal data

This paper presents an approach for detecting local damage in large scale frame structures by utilizing regularization methods for ill-posed problems. A direct relationship between the change in stiffness caused by local damage and the measured modal data for the damaged structure is developed, based on the perturbation method for structural dynamic systems. Thus, the measured incomplete modal data can be directly adopted in damage identification without requiring model reduction techniques, and common regularization methods could be effectively employed to solve the developed equations. Damage indicators are appropriately chosen to reflect both the location and severity of local damage in individual components of frame structures such as in brace members and at beam-column joints. The Truncated Singular Value Decomposition solution incorporating the Generalized Cross Validation method is introduced to evaluate the damage indicators for the cases when realistic errors exist in modal data measurements. Results for a 16-story building model structure show that structural damage can be correctly identified at detailed level using only limited information on the measured noisy modal data for the damaged structure.

Estimating trophic link density from quantitative but incomplete diet data

The trophic link density and the stability of food webs are thought to be related, but the nature of this relation is controversial. This article introduces a method for estimating the link density from diet tables which do not cover the complete food web and do not resolve all diet items to species level. A simple formula for the error of this estimate is derived. Link density is determined as a function of a threshold diet fraction below which diet items are ignored (

A BAYESIAN SHRINKAGE MODEL FOR INCOMPLETE LONGITUDINAL BINARY DATA WITH APPLICATION TO THE BREAST CANCER PREVENTION TRIAL

We consider inference in randomized studies, in which repeatedly measured outcomes may be informatively missing due to drop out. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and posit an exponential tilt model that links non-identifiable and identifiable distributions. This model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated and applied to data from the Breast Cancer Prevention Trial.

Using incomplete citation data for MEDLINE results ranking.

Information overload is a significant problem for modern medicine. Searching MEDLINE for common topics often retrieves more relevant documents than users can review. Therefore, we must identify documents that are not only relevant, but also important. Our system ranks articles using citation counts and the PageRank algorithm, incorporating data from the Science Citation Index. However, citation data is usually incomplete. Therefore, we explore the relationship between the quantity of citation information available to the system and the quality of the result ranking. Specifically, we test the ability of citation count and PageRank to identify "important articles" as defined by experts from large result sets with decreasing citation information. We found that PageRank performs better than simple citation counts, but both algorithms are surprisingly robust to information loss. We conclude that even an incomplete citation database is likely to be effective for importance ranking.

Using incomplete citation data for MEDLINE results ranking.

Information overload is a significant problem for modern medicine. Searching MEDLINE for common topics often retrieves more relevant documents than users can review. Therefore, we must identify documents that are not only relevant, but also important. Our system ranks articles using citation counts and the PageRank algorithm, incorporating data from the Science Citation Index. However, citation data is usually incomplete. Therefore, we explore the relationship between the quantity of citation information available to the system and the quality of the result ranking. Specifically, we test the ability of citation count and PageRank to identify "important articles" as defined by experts from large result sets with decreasing citation information. We found that PageRank performs better than simple citation counts, but both algorithms are surprisingly robust to information loss. We conclude that even an incomplete citation database is likely to be effective for importance ranking.

Multiemployer pension plan data are inaccurate and incomplete : report /

"B-209057"--Prelim. p.

Incomplete participant data affect reliability of values placed by actuaries on multiemployer pension plans : report to the Congress /

"September 6, 1984."

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamics of pattern writing and erasure in photorefractive lithium niobate for data storage applications

The present rate of technological advance continues to place significant demands on data storage devices. The sheer amount of digital data being generated each year along with consumer expectations, fuels these demands. At present, most digital data is stored magnetically, in the form of hard disk drives or on magnetic tape. The increase in areal density (AD) of magnetic hard disk drives over the past 50 years has been of the order of 100 million times, and current devices are storing data at ADs of the order of hundreds of gigabits per square inch. However, it has been known for some time that the progress in this form of data storage is approaching fundamental limits. The main limitation relates to the lower size limit that an individual bit can have for stable storage. Various techniques for overcoming these fundamental limits are currently the focus of considerable research effort. Most attempt to improve current data storage methods, or modify these slightly for higher density storage. Alternatively, three dimensional optical data storage is a promising field for the information storage needs of the future, offering very high density, high speed memory. There are two ways in which data may be recorded in a three dimensional optical medium; either bit-by-bit (similar in principle to an optical disc medium such as CD or DVD) or by using pages of bit data. Bit-by-bit techniques for three dimensional storage offer high density but are inherently slow due to the serial nature of data access. Page-based techniques, where a two-dimensional page of data bits is written in one write operation, can offer significantly higher data rates, due to their parallel nature. Holographic Data Storage (HDS) is one such page-oriented optical memory technique. This field of research has been active for several decades, but with few commercial products presently available. Another page-oriented optical memory technique involves recording pages of data as phase masks in a photorefractive medium. A photorefractive material is one by which the refractive index can be modified by light of the appropriate wavelength and intensity, and this property can be used to store information in these materials. In phase mask storage, two dimensional pages of data are recorded into a photorefractive crystal, as refractive index changes in the medium. A low-intensity readout beam propagating through the medium will have its intensity profile modified by these refractive index changes and a CCD camera can be used to monitor the readout beam, and thus read the stored data. The main aim of this research was to investigate data storage using phase masks in the photorefractive crystal, lithium niobate (LiNbO3). Firstly the experimental methods for storing the two dimensional pages of data (a set of vertical stripes of varying lengths) in the medium are presented. The laser beam used for writing, whose intensity profile is modified by an amplitudemask which contains a pattern of the information to be stored, illuminates the lithium niobate crystal and the photorefractive effect causes the patterns to be stored as refractive index changes in the medium. These patterns are read out non-destructively using a low intensity probe beam and a CCD camera. A common complication of information storage in photorefractive crystals is the issue of destructive readout. This is a problem particularly for holographic data storage, where the readout beam should be at the same wavelength as the beam used for writing. Since the charge carriers in the medium are still sensitive to the read light field, the readout beam erases the stored information. A method to avoid this is by using thermal fixing. Here the photorefractive medium is heated to temperatures above 150�C; this process forms an ionic grating in the medium. This ionic grating is insensitive to the readout beam and therefore the information is not erased during readout. A non-contact method for determining temperature change in a lithium niobate crystal is presented in this thesis. The temperature-dependent birefringent properties of the medium cause intensity oscillations to be observed for a beam propagating through the medium during a change in temperature. It is shown that each oscillation corresponds to a particular temperature change, and by counting the number of oscillations observed, the temperature change of the medium can be deduced. The presented technique for measuring temperature change could easily be applied to a situation where thermal fixing of data in a photorefractive medium is required. Furthermore, by using an expanded beam and monitoring the intensity oscillations over a wide region, it is shown that the temperature in various locations of the crystal can be monitored simultaneously. This technique could be used to deduce temperature gradients in the medium. It is shown that the three dimensional nature of the recording medium causes interesting degradation effects to occur when the patterns are written for a longer-than-optimal time. This degradation results in the splitting of the vertical stripes in the data pattern, and for long writing exposure times this process can result in the complete deterioration of the information in the medium. It is shown in that simply by using incoherent illumination, the original pattern can be recovered from the degraded state. The reason for the recovery is that the refractive index changes causing the degradation are of a smaller magnitude since they are induced by the write field components scattered from the written structures. During incoherent erasure, the lower magnitude refractive index changes are neutralised first, allowing the original pattern to be recovered. The degradation process is shown to be reversed during the recovery process, and a simple relationship is found relating the time at which particular features appear during degradation and recovery. A further outcome of this work is that the minimum stripe width of 30 ìm is required for accurate storage and recovery of the information in the medium, any size smaller than this results in incomplete recovery. The degradation and recovery process could be applied to an application in image scrambling or cryptography for optical information storage. A two dimensional numerical model based on the finite-difference beam propagation method (FD-BPM) is presented and used to gain insight into the pattern storage process. The model shows that the degradation of the patterns is due to the complicated path taken by the write beam as it propagates through the crystal, and in particular the scattering of this beam from the induced refractive index structures in the medium. The model indicates that the highest quality pattern storage would be achieved with a thin 0.5 mm medium; however this type of medium would also remove the degradation property of the patterns and the subsequent recovery process. To overcome the simplistic treatment of the refractive index change in the FD-BPM model, a fully three dimensional photorefractive model developed by Devaux is presented. This model shows significant insight into the pattern storage, particularly for the degradation and recovery process, and confirms the theory that the recovery of the degraded patterns is possible since the refractive index changes responsible for the degradation are of a smaller magnitude. Finally, detailed analysis of the pattern formation and degradation dynamics for periodic patterns of various periodicities is presented. It is shown that stripe widths in the write beam of greater than 150 ìm result in the formation of different types of refractive index changes, compared with the stripes of smaller widths. As a result, it is shown that the pattern storage method discussed in this thesis has an upper feature size limit of 150 ìm, for accurate and reliable pattern storage.