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A 'Compton' detector finds the direction of an X-ray by letting it interact with a gaseous, liquid or thin solid material (Tracker) and employing no collimators. This paper takes into account the case of an 'incomplete' solid Tracker where the recoiling electron travels only a few dozen microns and cannot be followed. However, impact positions and incoming and outgoing energies are measured. In this situation, exploiting the Compton Scattering formula, one is only able to identify a cone whose surface the X-ray belongs to. On the other hand, Compton tomography luckily requires only a few views (for example rotating the apparatus in just four positions around the subject), as the 'electronic collimation' that takes place in each position already extracts X-rays coming from many directions. A back-projection algorithm that combines the reconstructed 'cones' in space, weighed according to the Klein-Nishina formula, has been applied to the special case of small animal SPECT (Single Photon Emission Computed Tomography). Here the source is close to the detector, every imaged point in space is calculated from many rays that are emitted at different angles, and the algorithm totally differs from that of the Compton imaging in Astronomy. Tomography reconstruction has been validated by employing simulated data, generated using GEANT4 that includes the Doppler Broadening in the energies of scattered photons, which is due to moving non-free electrons. Space resolution has been assessed. [ABSTRACT FROM AUTHOR]

Image reconstruction for electrical capacitance tomography is to retrieve the permittivity distribution of processes with different dielectric materials inside from the measured capacitances outside. It is a typical inverse problem and has been always a challenge for its nonlinearity and ill-posedness. This paper explores the possibility of applying Tikhonov regularization, widely used for ill-posed problems, to the image reconstruction for electrical capacitance tomography. Two methods using different regularization matrices are investigated by using the simulated data, which are the standard Tikhonov regularization and the Tikhonov regularization based on the second order derivative operator. Results show that both the standard Tikhonov regularization and the Tikhonov regularization with the second order derivative operator do not provide reconstructions with qualities good enough. In order to improve this, a hybrid image reconstruction algorithm, which is based on the Tikhonov regularization with the reconstruction from the linear back projection as a constraint, is developed. Numerical results show that this hybrid image reconstruction algorithm takes advantages from both the linear back projection and the Tikhonov regularization and provide reconstructions better than those from the LBP and the Tikhonov regularization. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper presents a regularization method by using different window functions as regularization for electrical capacitance tomography (ECT) image reconstruction. Image reconstruction for ECT is a typical ill-posed inverse problem. Because of the small singular values of the sensitivity matrix, the solution is sensitive to the measurement noise. The proposed method uses the spectral filtering properties of different window functions to make the solution stable by suppressing the noise in measurements. The window functions, such as the Hanning window, the cosine window and so on, are modified for ECT image reconstruction. Simulations with respect to five typical permittivity distributions are carried out. The reconstructions are better and some of the contours are clearer than the results from the Tikhonov regularization. Numerical results show that the feasibility of the image reconstruction algorithm using different window functions as regularization. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Electrical capacitance tomography (ECT) is a non-invasive measurement technique that estimates the dielectric permittivity distribution of an inhomogeneous object from the boundary potentials at floating electrodes/or mutual capacitances. In this paper, a stochastic inverse technique based on genetic algorithm (GA-ECT) is developed, which is adapted to the two different methods, i.e. potential measurement and capacitance measurement. Numerical simulation results are presented to evaluate the inverse technique both for noise free and noisy data and the results show that quantitative image can be reconstructed not only with the low permittivity contrast but also with the high contrast. Furthermore, the influence of a priori knowledge to image reconstruction is discussed. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, we focus on data-limited tomographic imaging problems where the underlying linear inverse problem is ill-posed. A typical regularized reconstruction algorithm uses algebraic formulation with a predetermined discretization resolution. If the selected resolution is too low, we may loose useful details of the underlying image and if it is too high, the reconstruction will be unstable and the representation will fit irrelevant features. In this work, two approaches are introduced to address this issue. The first approach is using Mallow’s CL method or generalized cross-validation. For each of the two methods, a joint estimator of regularization parameter and discretization resolution is proposed and their asymptotic optimality is investigated. The second approach is a Bayesian estimator of the model order using a complexity-penalizing prior. Numerical experiments focus on a space imaging application from a set of limited-angle tomographic observations. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]