Discrete Tomography Reconstruction Research Articles

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography (DT) is a technology that uses image projection to reconstruct images. Its reconstruction problem, especially the binary image (0–1 matrix) has attracted strong attention. In this study, a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructed model. The solution process can be divided into two procedures. First, the DT problem is reformulated into a polyhedron judgment problem based on lattice basis reduction. Second, the fixed-point iterative method of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program. All the programs involved in this study are written in MATLAB. The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency, especially in the case of high dimension. The branch and bound method requires more branch operations and takes a long time. It also needs to store a large number of leaf node boundaries and the corresponding consumption matrix, which occupies a large memory space.

IDART: An Improved Discrete Tomography Algorithm for Reconstructing Images With Multiple Gray Levels.

The discrete algebraic reconstruction technique has many advantages in computed tomography and electron tomography. However, the number of gray levels and the absolute gray values that should be known in advance are typically not available in experiments especially when there are many gray levels in the image. In this paper, we report an automatic discrete tomography reconstruction algorithm to improve its feasibility in practice, without needing to know these two parameters. In our algorithm, the number of gray levels is estimated by labeling the connected components in the tomogram and the absolute values of them are determined by the modal value of each domain. The proposed algorithm was extensively validated on both simulated and experimental datasets. The results show that our algorithm can accurately recover not only the morphology but also the gray levels of the interested objects, even in the images with multiple gray levels. It is demonstrated that the presented algorithm is robust for eliminating missing wedge artifacts and tolerable for noisy data.

Regularized graph cuts based discrete tomography reconstruction methods

The topic of this paper includes graph cuts based computed tomography reconstruction methods in binary and multi-gray level cases. This approach combines the graph cuts and a gradient based method. The present paper introduces and analyses the shape circularity as a new regularization and incorporates it in a graph cuts based computed tomography reconstruction approach, thus introducing a new energy-minimization based reconstruction algorithm for binary tomography. Proposed method is capable for reconstructions in cases of limited projection view availability. Results of experimental evaluation of the considered graph cuts type reconstruction methods for both binary and multi-level tomography are presented.

Quantitative probing of the fast particle motion during the solidification of battery electrodes

Synchrotron x-ray tomography represents one of the most powerful imaging techniques that can visualize the three-dimensional microstructural complexity with a high spatial resolution. To date, however, the temporal resolution of this technique has been handicapped by the intrinsic limitations in the data acquisition speed and the lack of a suitable data processing method. The present study aims to fundamentally resolve this challenge by implementing a data analysis method that is based on differentiating discrete tomography reconstruction from a continuous scan reconstruction. With this methodological development, we capture and quantify the particle motion during the solidification of battery electrodes and reveal the statistics of the dynamically evolving motion in the drying process, which has been challenging to resolve. We discover that the particle motion exhibits a strong dependence on its geometric location within a drying electrode. Our results also imply that the final electrode quality can be controlled by balancing the solvent evaporation rate and the particle mobility in the region close to the drying surface.

Inline discrete tomography system: Application to agricultural product inspection

X-ray Computed Tomography (CT) has been applied in agriculture engineering for quality and defect control in food products. However, conventional CT systems are neither cost effective nor flexible, making the deployment of such technology unfeasible for many industrial environments. In this work, we propose a simple and cost effective X-ray imaging setup that comprises a linear translation of the object in a conveyor belt with a fixed X-ray source and detector, with which a small number of X-ray projections can be acquired within a limited angular range. Due to the limitations of such geometry, conventional reconstruction techniques lead to misshapen images. Therefore, we apply a Discrete Tomography reconstruction technique that incorporates prior knowledge of the density of the object’s materials. Moreover, we further improve the reconstruction results with the following strategies: (i) an image acquisition involving object rotation during a linear translation in the conveyor-belt; and (ii) an image reconstruction incorporating prior knowledge of the object support (e.g., obtained from optic sensors). Experiments based on simulation as well as real data demonstrate substantial improvement of the reconstruction quality compared to conventional reconstruction methods.

Accurate stochastic reconstruction of heterogeneous microstructures by limited x‐ray tomographic projections

An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for its performance prediction, prognosis and optimization. X-ray tomography has provided a nondestructive means for microstructure characterization in 3D and 4D (i.e. structural evolution over time), in which a material is typically reconstructed from a large number of tomographic projections using filtered-back-projection (FBP) method or algebraic reconstruction techniques (ART). Here, we present in detail a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of absorption contrast x-ray tomographic projections. This discrete tomography reconstruction procedure is in contrast to the commonly used FBP and ART, which usually requires thousands of projections for accurate microstructure rendition. The utility of our stochastic procedure is first demonstrated by reconstructing a wide class of two-phase heterogeneous materials including sandstone and hard-particle packing from simulated limited-angle projections in both cone-beam and parallel beam projection geometry. It is then applied to reconstruct tailored Sn-sphere-clay-matrix systems from limited-angle cone-beam data obtained via a lab-scale tomography facility at Arizona State University and parallel-beam synchrotron data obtained at Advanced Photon Source, Argonne National Laboratory. In addition, we examine the information content of tomography data by successively incorporating larger number of projections and quantifying the accuracy of the reconstructions. We show that only a small number of projections (e.g. 20-40, depending on the complexity of the microstructure of interest and desired resolution) are necessary for accurate material reconstructions via our stochastic procedure, which indicates its high efficiency in using limited structural information. The ramifications of the stochastic reconstruction procedure in 4D materials science are also discussed.

Deterministic discrete tomography reconstruction by energy minimization method on the triangular grid

In this paper we consider the binary tomography reconstruction problem on the triangular grid. A deterministic energy-minimization method is proposed. The new method is based on the convex–concave regularization approach and uses the Spectral Projected Gradient optimization algorithm. The proposed method shows significant advantages, regarding the quality of the reconstructions and required running time, in comparison with the previously suggested reconstruction method based on the stochastic Simulated Annealing algorithm. Experimental results, using regular hexagon shaped test images, are presented and analyzed.

Two-dimensional ion temperature measurement by application of tomographic reconstruction to Doppler spectroscopy

A novel 2D ion temperature measurement for toroidal plasmas has been developed by use of cost-effective discrete tomography reconstruction of 2D ion Doppler spectroscopy composed of a polychromator with an ICCD camera and optical fibres. The 2D projection of the line spectrum collected by 35 (7 × 5) optical fibres is transformed into the r–z profile of the local spectrum by means of the Abel inversion at each wavelength and finally into the 2D (r–z) profile of the ion temperature. Numerical tests of its algorithm indicate that the reconstruction error for a peaked temperature profile is smaller than 15% if the chord-integrated signals have noise smaller than 5%. This system successfully measured the peaked ion temperature profile of a torus plasma on the r–z plane under the condition of negligibly small plasma flow.

An island strategy for memetic discrete tomography reconstruction

In this paper we present a parallel island model memetic algorithm for binary discrete tomography reconstruction that uses only four projections without any further a priori information. The underlying combination strategy consists in separated populations of agents that evolve by means of different processes. Agents progress towards a possible solution by using genetic operators, switch and a particular compactness operator. A guided migration scheme is applied to select suitable migrants by considering both their own and their sub-population fitness. That is, from time to time, we allow some individuals to transfer to different subpopulations. The benefits of this paradigm were tested in terms of correctness, robustness and time of the reconstruction by considering publicly available datasets of images. To tackle the so-called stability problem, we considered the case of noisy projections along four directions to simulate an instrumental error. Results show that the proposed method decreases the reconstruction error for all classes of images with respect to a serial implementation recently proposed by the authors, and that such reconstruction error is almost invariant with respect to the number of demes. Moreover, the computation time of the proposed parallel memetic algorithm scales in a quasi-linear manner with respect to the demes number, and is invariant with respect to the used number of migrations.

Direction-dependency of binary tomographic reconstruction algorithms

In this work we study the relation between the quality of a binary tomographic reconstruction and the choice of angles of the projections. We conduct experiments on a set of software phantoms by reconstructing them from different projection sets using three different discrete tomography reconstruction algorithms, and compare the accuracy of the corresponding reconstructions with suitable approaches. To validate our results for possible real-world applications, we conduct the experiments by adding random noise of different characteristics to the simulated projection data, and by applying small topological changes on the phantom images as well. In addition, we also discuss some consequences of the angle-selection dependency and possible practical applications arising from the field of non-destructive testing, too.

DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING

We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,we want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions. Discrete Tomography (DT) deals with the reconstruction of digital images from their projections. The projections of an image are defined by the number of pixels of the colors on each line. Digital images are most commonly represented by inte- ger matrices. The problem of reconstructing monocolored images (blackand white) from two projections is well known (14). However, image processing in general and image reconstruction in particular is often characterized by uncertain and possi- bly inconsistent information. Since fuzzy programming is considered appropriate for solving real-world problems it seems reasonable to apply fuzzy programming methods to the reconstruction problem. In this paper, we propose a fuzzy approach for reconstructing binary images, which, instead of reconstructing projections exactly as in the deterministic recon- struction problem, recovers them as much as possible. The remainder of this paper is organized as follows. First, in Section 2, we briefly review fuzzy set theory and fuzzy programming and then, in Section 3, we present the problem of discrete tomography and image reconstruction. In Section 4, we discuss the application of fuzzy programming in image reconstruction and finally conclude the last section with a summary of our results.

A genetic algorithm for discrete tomography reconstruction

The aim of this paper is the description of an experiment carried out to verify the robustness of two different approaches for the reconstruction of convex polyominoes in discrete tomography. This is a new field of research, because it differs from classic computerized tomography, and several problems are still open. In particular, the stability problem is tackled by using both a modified version of a known algorithm and a new genetic approach. The effect of both, instrumental and quantization noises has been considered too.

Discrete tomography for reconstruction from limited view angles in non-destructive testing

Abstract We show that discrete tomography (DT) is suitable to increase the possible inspection size of single material oblong objects compared to filtered back projection (FBP) in non-destructive testing (NDT) with 2D X-ray computed tomography (CT). For such objects which are in one dimension larger than the maximum detectable material thickness limited view angles occur and FBP is not suitable for reconstruction. For evaluation of the reconstruction performance a copper phantom (strong absorber) which exhibits typical problems for NDT was manufactured. The increase of the object size with DT reconstruction compared to FBP was estimated to be above 50%.

Discrete tomography in neutron radiography

Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori information (such as an approximate shape of the object) we can apply two DT methods in neutron imaging by reducing the problem to an optimization task. The first method is a special one because it is only suitable if the object is composed of cylinders and sphere shapes. The second method is a general one in the sense that it can be used for reconstructing objects of any shape. Software was developed and physical experiments performed in order to investigate the effects of several reconstruction parameters: the number of projections, noise levels, and complexity of the object to be reconstructed. We give a summary of the experimental results and make a comparison of the results obtained using a classical reconstruction technique (FBP). The programs we developed are available in our DT reconstruction program package DIRECT.

Preliminary studies of discrete tomography in neutron imaging

Discrete tomography (DT) is a new technique to reconstruct discrete images from their projections (like neutron images). The reconstruction methods in DT are different from the conventional ones, because the created images may contain only a few numbers of given discrete values. One of the main reasons to apply DT is that hopefully we need only a few numbers of projections. In many applications we have a situation where we know the material components of the object to be studied, that is, we know the discrete values of the image to be reconstructed. Using discreteness and some a priori information we can apply several DT methods in neutron imaging. Most of the DT reconstruction methods are reducing the problem to an optimization task. We tried two such methods on software and physical phantoms. In these experiments we investigated the effects of the following parameters: number of projections, noise levels, and complexity of the object to be reconstructed. We also developed a software system, called DIRECT, for testing different DT methods, to compare them and to present the reconstructed objects.

Binary steering in discrete tomography reconstruction with sequential and simultaneous iterative algorithms

The binary steering process is a heuristic designed to intervene between consecutive steps of a nonbinary iterative image reconstruction algorithm in order to gradually steer the iterates towards a binary solution. We present computational results which show that a strongly overrelaxed simultaneous nonbinary iterative algorithm performs in our experiments better than a strongly underrelaxed sequential iterative algorithm. We also notice that faster binary steering gives better binary reconstructed images when the sequential iterative nonbinary algorithm is used.