1,721,019 research outputs found
4D Dual-Tree Complex Wavelets for Time-Dependent Data
Full text linkThe dual-tree complex wavelet transform (DT-WT) is extended to
the 4D setting. Key properties of 4D DT-WT, such as directional
sensitivity and shift-invariance, are discussed and illustrated in a
tomographic application. The inverse problem of reconstructing a dynamic
three-dimensional target from X-ray projection measurements can be formulated
as 4D space-time tomography. The results suggest that 4D DT-WT
offers simple implementations combined with useful theoretical properties for
tomographic reconstruction
Controlled wavelet domain sparsity for x-ray tomography
Full text linkTomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter mu > 0 is analogous to the notoriously difficult problem of picking the optimal regularization parameter in Tikhonov regularization. Here, a novel automatic method is introduced for choosing mu, based on a control algorithm driving the sparsity of the reconstruction to an a priori known ratio of nonzero versus zero wavelet coefficients in the unknown.Peer reviewe
Direct inversion from partial-boundary data in electrical impedance tomography
Full text linkIn electrical impedance tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse conductivity problem, in two dimensions and under the realistic assumption that only a part of the boundary is accessible to measurements. In this framework our data are modeled as a partial Neumann-to-Dirichlet map (ND map). We compare this data to the full-boundary ND map and prove that the error depends linearly on the size of the missing part of the boundary. The same linear dependence is further proved for the difference of the reconstructed conductivities - from partial and full boundary data. The reconstruction is based on a truncated and linearized D-bar method. Auxiliary results include an extrapolation method to estimate the full-boundary data from the measured one, an approximation of the complex geometrical optics solutions computed directly from the ND map as well as an approximate scattering transform for reconstructing the conductivity. Numerical verification of the convergence results and reconstructions are presented for simulated test cases
Multiresolution Parameter Choice Method With Total Variation Based Regularization In Image Denoising
Full text linkThis thesis will present a basic total variation based image denoising method which in applied mathematics is a specic case of a large group of problems called inverse problems. This study will specically concentrate on choosing a suitable regularization parameter and aims to investigate whether it could be automatically done by a method which was introduced in a paper called "Multiresolution Parameter Choice Method for Total Variation Regularized Tomography" (Kati Niinimäki, Lassas, Keijo Hämäläinen, Aki Kallonen, Ville Kolehmainen, Esa Niemi, and Samuli Siltanen. SIAM J. IMAGING SCIENCES 2016). I will go through the theoretical basic concepts regarding total variation based regularization and inverse problems in general. Finally I will introduce a new automatic parameter choice method candidate proposed by my supervisor, Samuli Siltanen, and gather some results how well it performs with the given task in practice
A variational reconstruction method for undersampled dynamic x-ray tomography based on physical motion models
Full text linkIn this paper we study the reconstruction of moving object densities from undersampled dynamic x-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a space-time reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation.
We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of results are presented for simulated and real measurement data with different sampling strategy. A key observation is that random sampling combined with our model allows reconstructions of similar amount of measurements and quality as a single static reconstruction
PROPAGATION AND RECOVERY OF SINGULARITIES IN THE INVERSE CONDUCTIVITY PROBLEM
Full text linkThe ill-posedness of Calderon's inverse conductivity problem, responsible for the poor spatial resolution of electrical impedance tomography (EIT), has been an impetus for the development of hybrid imaging techniques, which compensate for this lack of resolution by coupling with a second type of physical wave, typically modeled by a hyperbolic PDE. We show in two dimensions how, using EIT data alone, to use propagation of singularities for complex principal-type PDEs to efficiently detect interior jumps and other singularities of the conductivity. Analysis of variants of the CGO solutions of Astala and Paivarinta (Ann. Math. (2) 163: 1 (2006), 265-299) allows us to exploit a complex principal-type geometry underlying the problem and show that the leading term in a Born series is an invertible nonlinear generalized Radon transform of the conductivity. The wave front set of all higher-order terms can be characterized, and, under a prior, some refined descriptions are possible. We present numerics to show that this approach is effective for detecting inclusions within inclusions.Peer reviewe
Improved Passive Gamma Emission Tomography image quality in the central region of spent nuclear fuel
Full text linkReliable non-destructive methods for verifying spent nuclear fuel are essential to draw credible nuclear safeguards conclusions from spent fuel. In Finland, spent fuel items are verified prior to the soon starting disposal in a geological repository with Passive Gamma Emission Tomography (PGET), a uniquely accurate method capable of rod-level detection of missing active material. The PGET device consists of two highly collimated detector banks, collecting gamma emission data from a 360° rotation around a fuel assembly. 2D cross-sectional activity and attenuation images are simultaneously computed. We present methods for improving reconstructed image quality in the central parts of the fuel. The results are based on data collected from 2017 to 2021 at the Finnish nuclear power plants with 10 fuel assembly types of varying characteristics, for example burnups from 5.7 to 55 GWd/tU and cooling times from 1.9 to 37 years. Data is acquired in different gamma energy windows, capturing the peaks of Cs-137 (at 662 keV) and Eu-154 (at 1274 keV), abundant isotopes in long-cooled spent nuclear fuel. Data from these gamma energy windows at well-chosen angles are used for higher-quality images, resulting in more accurate detection of empty rod positions. The method is shown to detect partial diversion of nuclear material also in the axial direction, demonstrated with a novel measurement series scanning over the edge of partial-length rods
Alternating minimisation for glottal inverse filtering
No full textA new method is proposed for solving the glottal inverse filtering (GIF) problem. The goal of GIF is to separate an acoustical speech signal into two parts: the glottal airflow excitation and the vocal tract filter. To recover such information one has to deal with a blind deconvolution problem. This ill-posed inverse problem is solved under a deterministic setting, considering unknowns on both sides of the underlying operator equation. A stable reconstruction is obtained using a double regularization strategy, alternating between fixing either the glottal source signal or the vocal tract filter. This enables not only splitting the nonlinear and nonconvex problem into two linear and convex problems, but also allows the use of the best parameters and constraints to recover each variable at a time. This new technique, called alternating minimization glottal inverse filtering (AM-GIF), is compared with two other approaches: Markov chain Monte Carlo glottal inverse filtering (MCMC-GIF), and iterative adaptive inverse filtering (IAIF), using synthetic speech signals. The recent MCMC-GIF has good reconstruction quality but high computational cost. The state-of-the-art IAIF method is computationally fast but its accuracy deteriorates, particularly for speech signals of high fundamental frequency (F0). The results show the competitive performance of the new method: With high F0, the reconstruction quality is better than that of IAIF and close to MCMC-GIF while reducing the computational complexity by two orders of magnitude.Peer reviewe
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