: Accurate evaluation of dimensions directly from tomographic images, restored from only few x-ray projections, made in a limited observation sector, is considered exploiting pipes wall thickness assessment like a typical example. Both experiments and simulations are used to extract main errors sources. It is taken from as known, that neglecting of the scattered radiation and beam hardening effects results in image blurring, strong artifacts and finally inaccurate sizing. The computerized technique is developed to simulate the contribution of scattered radiation and beam hardening for the purpose of their further extraction from projected data. After those accompanying effects extraction the iterative Bayesian techniques are applied to reconstruct images from the projections, using volumetric and/or shell representation of the objects like pipes. The achieved error of virtual pipe wall thickness assessment from 3D images can be as small as 300 µ k comparing to 1mm provided by modern techniques. Finally the conclusion was drawn that standard projection techniques using X-or Gamma rays in combination with X-ray film or imaging plates can be applied for the data acquisition to reconstruct finally wall thickness profiles in an in-field environment.

In transmission radiography, information about an object is obtained by irradiating the object and recording the transmitted radiation. The recorded radiation consists of a primary and a scattered component. Conventional models count only for the primary component carrying the information about the object structure. The scattered radiation is considered as a homogeneous background and described as a built-up. But for quantitative radiation technique a detailed knowledge about the contribution of the scattering component is necessary. Monte Carlo transport methods are used to simulate the distribution of scattered radiation produced within engineered components. Because most of these components are complex in geometry a coupling of a CAD-based object description with Monte Carlo transport methods is developed. The paper describes the stochastic simulation scheme and compares the results with standard Monte Carlo codes like MCNP.

Standard radiography simulators are based on the attenuation law complemented by built-up-factors (BUF) to describe the interaction of radiation with material. The assumption of BUF implies that scattered radiation reduces only the contrast in radiographic images but does not image object structures itself. This simplification holds for a wide range of applications like weld inspection as known from practical experience. But only a detailed description of the different underlying interaction mechanisms is capable to explain effects like mottling or others that every radiographer has experienced in practice. The application of the N-Particle Monte Carlo code MCNP is capable to handle primary and secondary interaction mechanisms contributing to the image formation process like photon interactions (absorption, incoherent and coherent scattering including electron-binding effects, pair production) and electron interactions (electron tracing including X-Ray fluorescence and Brems-strahlung production). Additionally it opens up possibilities like the separation of influencing factors and the understanding of the functioning of intensifying screen used in film radiography. The paper intends to discuss the opportunities in applying the Monte Carlo method to investigate special features in radiography in terms of selected examples. It is important to note that the use of Monte Carlo methods is a laboratory type of technique for basic investigations because of the enormous computing power that is needed. For in-field applications such as for inspection planing simplified models are of much greater importance and increasingly in use.

The paper presents a special reconstruction algorithm that is capable to monitor density differences in multi-phase flows. The flow cross section is represented as discrete dynamic random field. A fixed gray value is assigned to each flow phase characterizing the material property of the phase. The image model is given by a set of non-linear stochastic difference equations. The corresponding inversion task is not accessible by common tomographic techniques applying reconstruction algorithms like filtered backprojection or algebraic reconstruction technique (ART). The developed algorithm is based on the Kalman filter technique adopted to non-linear phenomena. The average velocity distribution together with the corresponding covariance matrix of the liquid flow through a pipe serves as prior information in statistical sense. To overcome the non-linearity in the process model as well as in the measurement model the statistical linearization technique is applied. Moreover the Riccati equation, giving the error covariance matrix, and the equation for the optimal gain coefficients can be solved in advance and later used in the filter equation. It turns out that the resulting reconstruction or filter algorithm is recursive, i.e. yielding the quasi-optimal solution to the formulated inverse problem at every reconstruction step by successively counting for the new information collected in the projections. The applicability of the developed algorithm is discussed in terms of characterizing or monitoring a multi-phase flow in a pipe.

Common tomographic techniques assign a measure of material properties to a discrete element in the object space in order to characterize a specimen. The discretization of the object space, i.e. the size of a single volume element, is limited by the sensing mechanisms and the equipment used for the data acquisition. In any case the result of reconstruction gives a statistical average of the accessed material property within the considered element in the object space. To evaluate the integrity of a component the determined measures have to be correlated with its mechanical properties. Considering modem materials like reinforced plastics or metal foams the mechanical properties of the component are not determined by every single structural element like a single fiber in a composite material. Moreover the ensemble average and correlation properties as a means of statistical measure of all structural elements form the mechanical properties of the component. Accordingly a statistical description of the material properties on a macroscopic scale allow the characterization of its mechanical behavior or lifetime. The paper presents a special reconstruction algorithm that allows the statistical description of complex object structures including its dynamical properties. The proposed algorithm is based on a modified Kalman filter using statistical prior. The introduced prior includes knowledge about the covariance properties as well as assumptions about the probability density distribution function of the object structure. The resulting filter is recursive giving the optimal or quasi-optimal solution of the related inverse problem at every reconstruction step. The applicability of the developed algorithm is discussed for the investigation of an aluminum foam specimen and compared to standard 3D CT.

. Standard radiography simulators are based on the attenuation law complemented by built-up-factors (BUF) to describe the interaction of radiation with material. The assumption of BUF implies that scattered radiation reduces only the contrast in radiographic images. This simplification holds for a wide range of applications like weld inspection as known from practical experience. But only a detailed description of the different underlying interaction mechanisms is capable to explain effects like mottling or others that every radiographer has experienced in practice. The application of Monte Carlo models is capable to handle primary and secondary interaction mechanisms contributing to the image formation process like photon interactions (absorption, incoherent and coherent scattering including electron-binding effects, pair production) and electron interactions (electron tracing including X-Ray fluorescence and Bremsstrahlung production). It opens up possibilities like the separation of influencing factors and the understanding of the functioning of intensifying screen used in film radiography. The paper discusses the opportunities in applying the Monte Carlo method to investigate special features in radiography in terms of selected examples.

The last two decades have seen the development of numerous new X-ray-based imaging techniques and applications. Improvements in hardware such as radiation sources and detectors, as well as in data analysis methods both in image processing and in image reconstruction, have yielded significant advances in X-ray techniques. The use of computers plays a key, role in extending the capabilities of X-ray NDT for example in high-speed computed tomography in real-time image enhancement, in automated defect recognition, and in the development of accurate X-ray inspection simulations. However the ability to generate information and to analyse the complexities introduced by typical inspection demands can quickly overload computational resources. The developments in computer hardware and parallel computing are beginning to manage the huge amount of data routinely produced and open up a number of new applications fields. Some examples show new capabilities in X-ray image,formation modelling and 3D-image generation. To overcome the difficulties of using tomographic, method is when there is only restricted access in industrial constructions, regularisation and Bayesian techniques are introduced that consider prior knowledge about the object and flaw structure. This allows a quantitative evaluation of components characterising flaws by their position, orientation, and size. The ability to model the details of the generation of radiation and its interaction with the complex geotmetry of the object under consideration provides for the first time a means to determine and quantify the an inspection. In future, advances in computer hardware and computer science will have a rapidly increasing impact on modern NDT, as we have learnt from the recent past.

Considering modem materials like reinforced plastics or metal foams the mechanical properties of the component are not determined by every single structural element like a single fiber in a composite. Moreover the ensemble mean and correlation properties of all structural elements form the mechanical properties of the component. Accordingly a statistical description of material proper-ties on a macroscopic scale allow to characterize its mechanical behavior or aging. State of the art tomographic techniques assign a measure of material properties to a volume element. The discretization, i.e. the volume or size of a single element, is limited mainly by the physical mechanisms and the equipment used for the data acquisition. In any case the result of reconstruction yields a statistical average within the considered volume element. To evaluate the integrity of the component the determined measures have to be correlated with the mechanical properties of the component. Special reconstruction algorithms are investigated that allow the statistical description of complex object structures including its dynamics. The algorithm is based on the Kalman filter using statistical prior. The prior includes knowledge about the covariance matrix as well as a prior assumption about the probability density distribution function. The resulting algorithm is recursive yielding a quasi-optimal solution at every reconstruction step. The applicability of the developed algorithm is discussed for the investigation of a specimen made from aluminum foam.

The task of this work is to develop a technique for optimal linear recursive tomographic image reconstruction allowing the combination of the reconstruction process with projection data acquisition. The image supposes to be a discrete random field given by a set of linear stochastic difference equations with time as an independent variable. The proposed technique is applicable those tomographic modalities, scan geometries, and acquisition patterns that allow the introduction of a linear observation with an additive noise component. As a result the Kalman filter approach in the time domain is employed and the reconstruction process is represented as the optimal linear recursive estimation procedure with the optimal solution on each reconstruction step. The recursive properties of the proposed algorithm allow the parallelization of the data acquisition process and the reconstruction task. The main restrictions for the application of the Kalman filter approach are given by the huge dimension of the problem and the strong requirements to the amount of prior knowledge introduced. To overcome these restrictions a pseudo Kalman filter approach is investigated. This approach is based on replacing the prior covariance matrix with an empirical one. The reduction of the amount of prior knowledge decreases the dimensionality of the problem as well as the convergence velocity of the algorithm. Introducing an optimized scheme for the data acquisition procedure can partially compensate the degradation of the convergence process.

The dynamic image reconstruction allows to combine the acquisition of projection data with the reconstruction task. The image is supposed to be a random field discrete in space. Taking into account the properties of the acquisition task, the data can be represented as a multi-dimensional discrete-time Markovian process. As a result the Kalman filter technique in the time domain is proposed for optimal linear dynamic reconstruction. The main restrictions for employing the Kalman filter approach consist in the huge dimension of the algorithm and the strong requirements to the introduced prior knowledge. The main goal of this paper is to investigate a pseudo Kalman filter algorithm that provides sufficient decrease of the dimension and reduction of the necessary amount of prior knowledge. The proposed approach is based on applying the regularization principle together with a recursive estimation procedure. The regularization principle allows to replace statistical prior by empirical prior. The appropriate convergence condition of the pseudo Kalman filter algorithm is obtained by introducing the regularization function. To increase the convergence velocity an optimal data acquisition procedure is proposed. The potential of the proposed algorithms are discussed in terms of reconstruction results for glass fiber cable and dynamic fields.

Shell methods for reconstruction of two- and three-dimensional doubly connected binary objects based on limited numbers of X-ray projections taken in small angles have been developed.

Nondestructive evaluation techniques are mainly used for two purposes. One of these tasks is quality control in the production process. The second task is concerned with the problem of aging constructions and material degradation to ensure the safe operation of industrial installations. In both cases NDE provides a snapshot of the actual system situation. Dynamic effects are almost neglected. But for system monitoring and process control it is necessary to investigate the dynamics of the system. The paper deals with special statistical reconstruction techniques that are capable to record the dynamic behavior of systems based on nondestructive evaluation techniques.

Nondestructive evaluation techniques are mainly used for two purposes, One of these tasks is quality control in the production process, The second task is concerned with the problem of aging constructions and material degradation to ensure the safe operation of industrial installations, In both cases NDE provides a snapshot of the actual system situation, Dynamic effects are almost neglected, But for system monitoring and process control it is necessary to investigate the dynamics of the system, The paper deals with special statistical reconstruction techniques that are capable to record the dynamic behavior of systems based on nondestructive evaluation techniques.

The restoration of crack images in welds calculated from few x-ray projections only is connected with uncertainties which may corrupt the final images, namely: lack of admissible x-ray projections, lack on the projections of data, which definitely indicate the presence of crack, the crack appearance in the projection is frequently hidden by the images of other defects like undercuts, lack of fusion, etc. A complete Bayesian based technique was developed for a multi-step reconstruction of 3D crack images from limited number of 2D projections and checked using simulated and experimental data. A specific equipment for simultaneous circular rotation and out-of-plane tube positioning in connection with a photo diode line camera was developed and tested for in-field inspection and used for measuring the x-ray projections. The Bayesian quasi-3D restoration with Gibbs prior is applied at the last step being preprocessed by the following procedure: estimate the noise level in the 2D images of the object and select for further processing those projections at which the crack indication exceeds the noise level, extract the crack indications from all selected 2D images, apply the “first step technique” to the extracted crack indications. The efficiency of the developed technique is demonstrated using the crack image restoration from real experimental data of a 168×8 mm welded steel pipe with a crack concomitant by an undercut.

A model is discussed which describes the generation of Bremsstrahlung in X-ray tubes using tabulated interaction cross sections. The model includes radiographic parameters like kilovoltage and filtering and technical parameters like target material and target angle to count also for absorption in the target itself. Additionally characteristic radiation is described by a simple model. With the help of a simulation tool the influence of parameters can be studied independently.

A computer package for the simulation of the X-ray imaging process in nondestructive evaluation (NDE) is presented. The components of the radiographic inspection system are considered independently, i.e. the characteristics of the source, the geometry and the material properties of objects and defects, as well as the imaging process itself. The model is based on a ray tracer technique describing the attenuation of the radiation. The scattering effect is included in terms of built-up factors. A CAD-interface provides the opportunity to arrange independent CAD objects, e.g. the component geometry or defect shapes, defining a testing scheme. Complicated defect shapes are created by a preprocessor, the built-up factors can be received from experiments or from a separate model using an efficient solution of the scattering problem based on the theory of Markovian processes with random structure.

Confidence ratings of ultrasonic testing techniques and methods of their determination are discussed. Recommendations for selecting reliability criteria have been tested in experiments.

A newly developed technique for the three-dimensional x-ray reconstruction of binary images is discussed. It allows one to reduce extremely (about 10-100 times) the number of required projections and views and to suppress the main artifacts. The technique is based upon the solution of an imposed operator equation using special types of functionals, which are also discussed. The steps for its solution provide the zero-level approximation, the computer simulation of the radiographic process and the use of the a priori knowledge about structural features in general form. They give the priority to planar and/or volumetric images in the matrix. The efficiency of corresponding functionals and algorithms is compared to the maximum-likelihood (ML) estimation using both simulated and real radiographic data. The introduced prior functionals are discussed in terms of Markov random fields and Gibbs statistics used for Bayesian image reconstruction with higher-order models as priors.

Here the 3D X-Ray Bayesian reconstruction (BR) with Gibbs priors (GP) is considered in the form of quadratic functional (QF) representation of two mechanical and one statistical model being applied to the problem of image restoration from strongly incomplete noisy data. The BR with GP in the form of mechanical modeis as priors can result in an image restoration using 10–100 times less number of projections compared to cone-beam Computer Tomography. The quality of reconstruction as well as the computing time are shown to be strongly dependent upon the form of the a priory model and the noise level. Additionally a new prior is introduced in terms of a statistical model. Results are presented investigating the influence of the applied GP form and the noise level on quality of the reconstruction procedure for which quantitative estimates are provided. Restoration capabilities are compared for three types of models: cluster, plane and phase support algorithm. The influence of the following variables involved in the reconstruction procedure of binary and three level object are investigated: (i) the number of cone-beam projections up to 36, (ii) the level of Gaussian distributed white noise imposed on the 2D projections having the variance up to the value four times larger than the grey level resulted from projecting of one defect voxel, (iii) the form of the prior constraint, (iv) the value of the regularization parameter, and (v) the zero-level approximation before starting the minimization procedure. The error of the reconstruction and the computing time are choosen to be the final estimators of the capability of the method in all cases. Finally, conclusions are drawn about the potential of the method for multi-step BR with GP.

Prior knowledge concerning information about the image and noise properties strongly influence the performance of image reconstruction from projections in computerized tomography. The authors propose an adaptive recursive 2D image reconstruction under uncertain conditions for the image and statistical noise properties. The Reconstruction is considered as adaptive estimation problem on the basis of empirical data generated by a predictive image model. The projection model is introduced by the vector y(n) given by the components \({{y}_{m}}(n) = \sum\nolimits_{{{{r}_{1}} = 1}}^{R} {\sum\nolimits_{{{{r}_{2}} = 1}}^{R} {{{x}_{{mr}}}} } (n){{a}_{r}} + {{\xi }_{m}}(n), r = {{r}_{1}},{{r}_{2}}\) with the random image values a r on a rectangular grid of size R× R, the number of current projection n(n =1, 2, 3, ⋯), the detector number m= 1, 2, ⋯ M, the elements of the M× R 2 projection matrix x mr (n), and the noise component ξ m (n). For the reconstruction step nonly the new information provided by the projection y m (n) (m= 1, 2, ⋯, M) and the previous estimations â r (k) (k= n− 1, n − 2, ⋯, n−1 − n 0) are used with predictive image model algorithm a* (n) = Φ [â (k), k = n− 1, ⋯, n− 1− n0] = Φ (â, n0), where n 0 gives the order of the prediction model. For the solution of this problem the cost function F(â, a, n) with the constraints Q m (â, y, n) = 0 is employed. Because the prior FDD function for the image parameters and the noise properties are unknown, the empirical PDD is used which is determined from predicted image data. Therefore the adaptive, empirical data-based estimation criteria has the form. The proposed reconstruction algorithm is applied to simulated and experimental projection data, and compared with standard CT algorithms.