Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate-combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 相似文献   

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.     

Reconstruction of smooth distributions within unsmooth circumferences from limited views using filtered‐backprojection algorithm

This study demonstrates the feasibility of reconstruction of smooth distributions within unsmooth circumferences from limited views using the filtered‐backprojection algorithm with angular interpolation in Fourier domain, which leads to noniterative reconstruction of smooth distributions within skulls in diagnostic medicine. Two phantoms with a circular and an elliptic circumference are numerically tested. This speedy approach has great advantages in applications when swift reaction is necessary or when result of reconstruction is indispensably navigational to its following detection. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 93–96, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10015     

An accelerated multiplicative iterative algorithm in image reconstruction

Based on the ML‐EM (maximum likelihood expectation maximization) algorithm and AWLS (one kind of multiplicative weighted least square) reconstruction, a new algorithm named RMITC (rapid multiplicative iteration with total‐count conservation) is proposed. The new method assumes a higher order correction factor and incorporates a total‐count conservation constraint to obtain better images reconstructed while achieving a higher speed of convergence. Computer simulated phantom data and real positron emission tomography (PET) transmission data were used to compare the new method with other reconstruction algorithms, such as ML‐EM and AWLS. Results demonstrated that the new method is faster and better quantitatively than both ML‐EM and AWLS. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 97–100, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10016     

Numerical integration of the stiff dynamics of geometrically exact shells: an energy‐dissipative momentum‐conserving scheme

This paper presents a new family of time‐stepping algorithms for the integration of the dynamics of non‐linear shells. We consider the geometrically exact shell theory involving an inextensible director field (the so‐called five‐parameter shell model). The main characteristic of this model is the presence of the group of finite rotations in the configuration manifold describing the deformation of the solid. In this context, we develop time‐stepping algorithms whose discrete solutions exhibit the same conservation laws of linear and angular momenta as the underlying physical system, and allow the introduction of a controllable non‐negative energy dissipation to handle the high numerical stiffness characteristic of these problems. A series of algorithmic parameters for the different components of the deformation of the shell (i.e. membrane, bending and transverse shear) fully control this numerical dissipation, recovering existing energy‐momentum schemes as a particular choice of these algorithmic parameters. We present rigorous proofs of the numerical properties of the resulting algorithms in the full non‐linear range. Furthermore, it is argued that the numerical dissipation is introduced in the high‐frequency range by considering the proposed algorithm in the context of a linear problem. The finite element implementation of the resulting methods is described in detail as well as considered in the final arguments proving the aforementioned conservation/dissipation properties. We present several representative numerical simulations illustrating the performance of the newly proposed methods. The robustness gained over existing methods in these stiff problems is confirmed in particular. Copyright © 2002 John Wiley & Sons, Ltd.     

Fixed‐lag smoothing and state estimation in dynamic electrical impedance tomography

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The conventional approach is to inject several different current patterns and use the associated data for the reconstruction of a single distribution. This is an ill‐posed inverse problem. In some applications the resistivity changes may be so fast that the target changes between the injection of the current patterns and thus the data do not correspond to the same target distribution. In these cases traditional reconstruction methods yield severely blurred resistivity estimates. We have earlier proposed to formulate the EIT problem as an augmented system theoretical state estimation problem. The reconstruction problem can then be solved with Kalman filter and Kalman smoother algorithms. In this paper, we use the so‐called fixed‐lag smoother to solve the dynamic EIT reconstruction problem. We show that data storage difficulties that are associated with the previously used fixed‐interval smoother can be avoided using the fixed‐lag smoother. The proposed methods are compared with simulated measurements and real data. Copyright © 2001 John Wiley & Sons, Ltd.     

An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics

We present in this paper a new finite element formulation of geometrically exact rod models in the three‐dimensional dynamic elastic range. The proposed formulation leads to an objective (or frame‐indifferent under superposed rigid body motions) approximation of the strain measures of the rod involving finite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod's cross‐section. Furthermore, the proposed framework allows the development of time‐stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod's dynamics. Several numerical simulations are presented illustrating these properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Segmentation for brain magnetic resonance images using dual‐tree complex wavelet transform and spatial constrained self‐organizing tree map

In brain MR images, the noise and low‐contrast significantly deteriorate the segmentation results. In this paper, we introduce a novel application of dual‐tree complex wavelet transform (DT‐CWT), and propose an automatic unsupervised segmentation method integrating DT‐CWT with self‐organizing map for brain MR images. First, a multidimensional feature vector is constructed based on the intensity, low‐frequency subband of DT‐CWT, and spatial position information. Then, a spatial constrained self‐organizing tree map (SCSOTM) is presented as the segmentation system. It adaptively captures the complicated spatial layout of the individual tissues, and overcomes the problem of overlapping gray‐scale intensities for different tissues. SCSOTM applies a dual‐thresholding method for automatic growing of the tree map, which uses the information from the high‐frequency subbands of DT‐CWT. The proposed method is validated by extensive experiments using both simulated and real T1‐weighted MR images, and compared with the state‐of‐the‐art algorithms. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 208–214, 2014     

Fast Feldkamp reconstruction based on focus of attention and distributed computing

The Feldkamp algorithm is widely accepted as a practical conebeam reconstruction method for three‐dimensional x‐ray computed tomography. We introduce focus of attention, an effective and simple to implement datadriven preprocessing scheme, for identifying a convex subset of voxels that include all those relevant to the object under study. By concentrating on this subset of voxels during reconstruction, we reduce the computational demands of the Feldkamp algorithm correspondingly. To achieve further speed‐up, all computations are distributed across a cluster of inexpensive, dual‐processor PCs. We present experimental work based on mouse data obtained from the MicroCAT which is a high‐resolution x‐ray computed tomography system for small animal imaging. This work shows that focus of attention can cut the overall computation time in half without affecting the image quality. The method is general by nature and can easily be adapted to apply to other geometries and modalities as well as to iterative reconstruction algorithms. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 12, 229–234, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10027     

Compton back-scattering imaging

A Compton back-scatter tomographical imaging model with minimal constraints was imposed as a potential contender for on-line portable imaging. The line-scan method based on scattered photon energy spectra can obtain a fairly high scan speed and spatial resolution. As such, radiation scattering imaging (or density reconstruction) is viewed as a nonlinear inverse problem. A multicriteria optimization-based density reconstruction from computed compton scattering data illustrates the feasibility of this method. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol 10, 410–414, 1999     

Optimization and integration of high‐performance ground penetrating imaging radar system: A research prototype

This paper reports the design, development, and field experimentation of a new ground penetrating imaging radar system. This research prototype unit features full system optimization, which successfully integrates the key components of antenna sensitivity, data‐acquisition waveforms, synthetic‐aperture scan, and image reconstruction algorithms, for optimal system performance.© 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 220–223, 2005     

A Fourier approach to the natural pixel discretization of brain single‐photon emission computed tomography

We apply the natural pixel (NP) approach to the single‐photon emission computed tomography (SPECT) problem. The NP approach allows us to split the tomographic problem into two subproblems. The first is a linear inverse problem. The data are the measured projections and the linear operator is described by a Gram matrix, and provides a set of coefficients. The second consists of computing the solution of the tomographic problem as a linear combination of the elements of the NP basis with respect to the coefficients obtained by solving the first problem, and it provides a solution for any given grid of points. The spatially varying geometric response of the system is taken into account by properly choosing the elements of the basis. The rotational invariance shown by the elements of the considered basis induces a block circulant structure in the Gram matrix. This structure can be used to reduce the computational efforts needed for solving the inverse problem. In particular, we diagonalize (blockwise) the Gram matrix by applying the discrete Fourier transform and we solve the inverse problem in the frequency domain associated with the rotation angles. We develop numerical validation with synthetic data in order to test the performance of the NP approach and to assess the reliability of the results. A reconstruction of a two‐dimensional image requires 45–94 s, which is an acceptable time for clinical purposes. Finally, we apply the method to acquired clinical data that consist of a three‐dimensional brain scan. © 2002 John Wiley & Sons, Inc. Int J Imaging Syst Technol 12, 1–8, 2002     

Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography

Diffraction tomography (DT) is an inversion scheme used to reconstruct the spatially variant refractive-index distribution of a scattering object. We developed computationally efficient algorithms for image reconstruction in three-dimensional (3D) DT. A unique and important aspect of these algorithms is that they involve only a series of two-dimensional reconstructions and thus greatly reduce the prohibitively large computational load required by conventional 3D reconstruction algorithms. We also investigated the noise characteristics of these algorithms and developed strategies that exploit the statistically complementary information inherent in the measured data to achieve a bias-free reduction of the reconstructed image variance. We performed numerical studies that corroborate our theoretical assertions.     

Cone-beam tomography with a digital camera

We show that x-ray computer tomography algorithms can be applied with minimal alteration to the three-dimensional reconstruction of visible sources. Diffraction and opacity affect visible systems more severely than x-ray systems. For camera-based tomography, diffraction can be neglected for objects within the depth of field. We show that, for convex objects, opacity has the effect of windowing the angular observation range and thus blurring the reconstruction. For concave objects, opacity leads to nonlinearity in the transformation from object to reconstruction and may cause multiple objects to map to the same reconstruction. In x-ray tomography, the contribution of an object point to a line integral is independent of the orientation of the line. In optical tomography, however, a Lambertian assumption may be more realistic. We derive an expression for the blur function (the patch response) for a Lambertian source. We present experimental results showing cone-beam reconstruction of an incoherently illuminated opaque object.     

Cubic spline algorithms for orientation interpolation

This article presents a class of spline algorithms for generating orientation trajectories that approximately minimize angular acceleration. Each algorithm constructs a twice‐differentiable curve on the rotation group SO(3) that interpolates a given ordered set of rotation matrices at specified knot times. Rotation matrices are parametrized, respectively, by the unit quaternion, canonical co‐ordinate, and Cayley–Rodrigues representations. All the algorithms share the common feature of (i) being invariant with respect to choice of fixed and moving frames (bi‐invariant), and (ii) being cubic in the parametrized co‐ordinates. We assess the performance of these algorithms by comparing the resulting trajectories with the minimum angular acceleration curve. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of γ‐α′‐Phase Transformation in Metastable Austenitic Steels on the Mechanical Behavior During Tensile and Fatigue Loading at Ambient and Lower Temperatures

The present investigation is concerned with the three metastable austenitic steels AISI 304 (X5CrNi1810), 321 (X6CrNiTi1810), and 348 (X10CrNiNb189). In the temperature range ?60 °C ≤ T ≤ 25 °C tensile and fatigue tests were performed to characterize the mechanical and phase transformation behavior using stress‐elongation, stress–strain hysteresis, and magnetic measurements. The mechanical properties are significantly influenced by the temperature dependent deformation induced phase transformation from austenite to α′‐martensite which are combined with pronounced hardening processes. Furthermore microhardness measurements after fracture could be correlated with the results of the fatigue tests.     

Time‐varying reconstruction in single photon emission computed tomography

We propose a new method for reconstruction of images in single photon emission computed tomography (SPECT), when the activity distribution of the object is time‐varying. The activity evolution is modeled with the first‐order Markov model, and linear observation model is used to characterize the measurement system. The state‐space representation of the measurement sequence reduces to an ill‐conditioned state estimation problem, which is solved recursively using the Kalman filter and smoother algorithms. Two special models, the compartmental model and the diffusion model, for the time variation are discussed. The method is evaluated using simulations. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 186–197, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20023     

Application of Krylov subspaces to SPECT imaging

The application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two‐dimensional case) to 15 (three‐dimensional case). On this basis, a new, proposed approach can be basically summarized as follows: construction of a basis spanning a Krylov subspace of suitable dimension and projection of the projector–backprojector matrix (a 10⁶ × 10⁶ matrix in the three‐dimensional case) onto such a subspace. In this way, one is led to a problem of low dimensionality, for which regularized solutions can be easily and quickly obtained. The required SPECT activity map is expanded as a linear combination of the basis elements spanning the Krylov subspace and the regularization acts by modifying the coefficients of such an expansion. By means of a suitable graphical interface, the tuning of the regularization parameter(s) can be performed interactively on the basis of the visual inspection of one or some slices cut from a reconstruction. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 217–228, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10026     

Minimal-scan filtered backpropagation algorithms for diffraction tomography

The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging 4, 336 (1982)], has been widely used for reconstructing images in diffraction tomography. It is generally known that the FBPP algorithm requires scattered data from a full angular range of 2 pi for exact reconstruction of a generally complex-valued object function. However, we reveal that one needs scattered data only over the angular range 0 < or = phi < or = 3 pi/2 for exact reconstruction of a generally complex-valued object function. Using this insight, we develop and analyze a family of minimal-scan filtered backpropagation (MS-FBPP) algorithms, which, unlike the FBPP algorithm, use scattered data acquired from view angles over the range 0 < or = phi < or = 3 pi/2. We show analytically that these MS-FBPP algorithms are mathematically identical to the FBPP algorithm. We also perform computer simulation studies for validation, demonstration, and comparison of these MS-FBPP algorithms. The numerical results in these simulation studies corroborate our theoretical assertions.     

Filtered backprojection algorithm can outperform iterative maximum likelihood expectation‐maximization algorithm

The iterative maximum‐likelihood expectation‐maximization (ML‐EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML‐EM in certain occasions, when the least‐squared difference from the true image, that is, the least‐squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML‐EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML‐EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML‐EM images. For the noiseless projections, the FBP algorithms outperform the ML‐EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML‐EM algorithm. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 114–120, 2012