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  • 951.
    Wahlberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Partizan Poset Games2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This thesis analyzes a class of element-removal partizan games played on colored posets. In these games a player moves by removing an element of its color together with all greater elements in the poset. A player loses if it has no elements left to remove.

    It is shown that all such games are numbers and that the dominating game options are to remove elements not lower than any other element of the same color.

    In particular, the thesis concerns games played on posets that are chess-colored Young diagrams. It is shown that it is easy to compute the value for any such game with < 3 rows by proving a proposed formula for computing the value.

  • 952.
    Weinberger, Oskar
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Realisations of heteroclinic networks in coupled cell systems2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In the theory of dynamical systems, heteroclinic networks are invariant objects in phase space with network structure, consisting of invariant sets (nodes) and connecting trajectories between them (edges). These are typically not robust dynamical phenomena, but can appear robustly for dynamical systems with network structure - so called coupled cell systems -due to the presence of certain synchrony related invariant subspaces. This link between networks in phase space and networks of dynamical systems is the topic of this thesis. Examples and results from the literature on the existence and construction of heteroclinic networks in coupled cell systems are presented and reviewed, focusing on heteroclinic realisation: how can coupled cell systems be constructed that support a given heteroclinic network? We seek to find explicit vector fields for such realisations, of which there are relatively few examples in the literature, and provide a polynomial vector field for a particular heteroclinic network and coupled system. Finally, we state and prove a theorem on the existence of additional equilibrium points for realisations of this heteroclinic network in such systems.

  • 953.
    Wennman, Aron
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Random and optimal configurations in complex function theory2018Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of six articles spanning over several areas of mathematical analysis. The dominant theme is the study of random point processes and optimal point configurations, which may be though of as systems of charged particles with mutual repulsion. We are predominantly occupied with questions of universality, a phenomenon that appears in the study of random complex systems where seemingly unrelated microscopic laws produce systems with striking similarities in various scaling limits. In particular, we obtain a complete asymptotic expansion of planar orthogonal polynomials with respect to exponentially varying weights, which yields universality for the microscopic boundary behavior in the random normal matrix (RNM) model (Paper A) as well as in the case of more general interfaces for Bergman kernels (Paper B). Still in the setting of RNM ensembles, we investigate properties of scaling limits near singular points of the boundary of the spectrum, including cusps points (Paper C). We also obtain a central limit theorem for fluctuations of linear statistics in the polyanalytic Ginibre ensemble, using a new representation of the polyanalytic correlation kernel in terms of algebraic differential operators acting on the classical Ginibre kernel (Paper D). Paper E is concerned with an extremal problem for analytic polynomials, which may heuristically be interpreted as an optimal packing problem for the corresponding zeros. The last article (Paper F) concerns a different theme, namely a sharp topological transition in an Lp-analogue of classical Carleman classes for 0 < p < 1.

  • 954.
    Wennman, Aron
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ameur, Yacin
    Kang, Nam-Gyu
    Makarov, Nikolai
    Scaling limits of random normal matrix processes at singular boundary pointsManuskript (preprint) (Annet vitenskapelig)
  • 955.
    Wennman, Aron
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hedenmalm, Håkan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Off-spectral analysis of Bergman kernelsManuskript (preprint) (Annet vitenskapelig)
  • 956.
    Wennman, Aron
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hedenmalm, Håkan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Planar orthogonal polynomials and boundary universality in the random normal matrix modelManuskript (preprint) (Annet vitenskapelig)
  • 957.
    Westerbäck, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Maximal partial packings of Z(2)(n) with perfect codes2007Inngår i: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 42, nr 3, s. 335-355Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A maximal partial Hamming packing of Z(2)(n) is a family S of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in S. The number of translates of Hamming codes in S is the packing number, and a partial Hamming packing is strictly partial if the family S does not constitute a partition of Z(2)(n). A simple and useful condition describing when two translates of Hamming codes are disjoint or not disjoint is proved. This condition depends on the dual codes of the corresponding Hamming codes. Partly, by using this condition, it is shown that the packing number p, for anymaximal strictly partial Hamming packing of Z(2)(n), n = 2(m)-1, satisfies m + 1 = 4, there exist maximal strictly partial Hamming packings of Z(2)(n) with packing numbers n- 10, n- 9, n- 8,..., n- 1. This implies that the upper bound is tight for any n = 2(m) - 1, m >= 4. All packing numbers for maximal strictly partial Hamming packings of Z(2)(n), n = 7 and 15, are found by a computer search. In the case n = 7 the packing number is 5, and in the case n = 15 the possible packing numbers are 5, 6, 7,..., 13 and 14.

  • 958.
    Westerbäck, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Parity check systems of codes over finite commutative Frobeniusrings and finite Abelian groupsArtikkel i tidsskrift (Annet vitenskapelig)
  • 959.
    Westerbäck, Thomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Parity check systems, perfect codes and codes over Frobenius rings2012Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis consists of five papers related to coding theory. The first four papers are mainly devoted to perfect 1-error correcting binary codes. The fifth paper concerns codes over finite Abelian groups and finite commutative Frobenius rings.

    In Paper A we construct a new class of perfect binary codes of length 15. These codes can not be obtained by a construction of Phelps and Solov’eva. The verification of the existence of these kind of codes gives an answer to a question by Zinoviev and Zinoviev from 2003.

    In Paper B the concept of extended equivalence for binary codes is introduced. A linear code L*C, which is an invariant for this equivalence relation, is associated with every perfect binary code C. By using L*C we give, in some particular cases, a complete enumeration of the extended equivalence classes of perfect binary codes.

    In Paper C and D we prove that there exist perfect binary codes and extended perfect binary codes with a trivial symmetry group for most admissible cases of lengths and ranks. The results of these two papers have, together with previously known results, completely solved the problem of for which lengths and ranks there exist perfect binary codes with a trivial symmetry group, except in a handful of cases.

    In Paper E the concept of parity check matrices of linear codes over finite fields is generalized to parity check systems of both linear and nonlinear codes over finite Abelian groups and finite commutative Frobenius rings. A parity check system is a concatenation of two matrices and can be found by the use of Fourier analysis over finite Abelian groups. It is shown how some fundamental properties of a code can be derived from the set of columns or the set of rows in an associated parity check system. Furthermore, in Paper E, Cayley graphs and integral group rings are associated with parity check systems in order to investigate some problems in coding theory.

  • 960.
    Wiegandt, Sebastian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On the Smoothness of the Quot Functor2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    For a commutative ring k,we consider free k-modules E, endowing them with k[x_1,...,x_m]-module structuresthrough a ring homomorphism k[x_1,...,x_m] -> End_Z(E). These structures arethen inspected by encoding the actions of the unknowns x_i in matricesX_1,...,X_m. We further introduce the concepts of lifts and formal smoothnessfor functors, and define the Quot_{F/A/k}^n functor acting on the category ofk-algebras, taking some k-algebra B to the set of quotients of the form (F ⊗_k B)/N, which are locallyfree as B-modules. Lastly, we find concrete examples of modules showing thatthe functors Hilb_{k[x,y,z]/k}^4 and Quot_{⊕^2 k[x,y]/k[x,y]/k}^2 are not formally smooth

  • 961. Wiener, L.
    et al.
    Ekholm, Tomas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Haller, Philipp
    KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.
    Modular responsive web design: An experience report2017Inngår i: Companion to the first International Conference on the Art, Science and Engineering of Programming, Association for Computing Machinery (ACM), 2017, Vol. F129681, artikkel-id a22Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Responsive Web Design (RWD) enables web applications to adapt to the characteristics of different devices such as screen size which is important for mobile browsing. Today, the only W3C standard to support this adaptability is CSS media queries. However, using media queries it is impossible to create applications in a modular way, because responsive elements then always depend on the global context. Hence, responsive elements can only be reused if the global context is exactly the same. This makes it extremely challenging to develop large responsive applications, because the lack of true modularity makes certain requirement changes either impossible or expensive to realize. In this paper we extend RWD to also include responsive modules, i.e., modules that adapt their design based on their local context, independently of the global context. We present the ELQ project that includes an approach to enabling modular responsivity, and a novel implementation of resize detection of DOM elements. ELQ provides an implementation of element queries which generalize CSS media queries. Importantly, our design conforms to existing web specifications, enabling adoption on a large scale. ELQ is designed to be heavily extensible using plugins. Experimental results show speed-ups of the core algorithms of up to 37x compared to previous approaches. CCS Concepts • Software and its engineering → Domain specific languages; Reusability; Hypertext languages;.

  • 962.
    Winckler, Björn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A renormalization fixed point for Lorenz maps2010Inngår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 23, nr 6, s. 1291-1302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A Lorenz map is a Poincare map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.

  • 963.
    Winckler, Björn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Renormalization of Lorenz Maps2011Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This thesis is a study of the renormalization operator on Lorenz αmaps with a critical point. Lorenz maps arise naturally as first-return maps for three-dimensional geometric Lorenz flows. Renormalization is a tool for analyzing the microscopic geometry of dynamical systems undergoing a phase transition.

    In the first part we develop new tools to study the limit set of renormalization for Lorenz maps whose combinatorics satisfy a long return condition. This combinatorial condition leads to the construction of a relatively compact subset of Lorenz maps which is essentially invariant under renormalization. From here we can deduce topological properties of the limit set (e.g. existence of periodic points of renormalization) as well as measure theoretic properties of infinitely renormalizable maps (e.g. existence of uniquely ergodic Cantor attractors). After this, we show how Martens’ decompositions can be used to study the differentiable structure of the limit set of renormalization. We prove that each point in the limit set has a global two-dimensional unstable manifold which is a graph and that the intersection of an unstable manifold with the domain of renormalization is a Cantor set. All results in this part are stated for arbitrary real critical exponents  α> 1.

    In the second part we give a computer assisted proof of the existence of a hyperbolic fixed point for the renormalization operator on Lorenz maps of the simplest possible nonunimodal combinatorial type. We then show how this can be used to deduce both universality and rigidity for maps with the same combinatorial type as the fixed point. The results in this part are only stated for critical exponenta α= 2.

  • 964. Wood, David R.
    et al.
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Thomassen's Choosability Argument Revisited2010Inngår i: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 24, nr 4, s. 1632-1637Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Thomassen (J. Combin. Theory Ser. B, 62 (1994), pp. 180-181) proved that every planar graph is 5-choosable. This result was generalized by. Skrekovski (Discrete Math., 190 (1998), pp. 223- 226) and He, Miao, and Shen (Discrete Math., 308 (2008), pp. 4024-4026), who proved that every K-5-minor-free graph is 5-choosable. Both proofs rely on the characterization of K-5-minor-free graphs due to Wagner (Math. Ann., 114 (1937), pp. 570-590). This paper proves the same result without using Wagner's structure theorem or even planar embeddings. Given that there is no structure theorem for graphs with no K-6-minor, we argue that this proof suggests a possible approach for attacking the Hadwiger Conjecture.

  • 965.
    Zackrisson, Samuel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Coefficients and zeros of mixed characteristicpolynomials2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The mixed characteristic polynomial (MCP) was introduced in the papersof Marcus, Spielman and Srivastava from 2013 on Ramanujan graphs and the Kadison-Singerconjecture. Several known results and open problems can be formulated in termsof MCPs. The proofs of Marcus, Spielman and Srivastava involve bounding theroots of certain MCPs. Gurvits’ generalization of van der Waerden’s permanentconjecture bounds the constant term of MCPs using the capacity of an underlyingpolynomial.This thesis surveys selected results for MCPs. A counterexample to theHolens-Ðoković conjecture, due to Wanless, is discussed in the context of MCPs.It is used to show how a sequence of MCP coefficients is not monotoneand how the roots of associated Laguerre polynomials do not always majorizethose of other MCPs. Finally, we prove an analogue of the root bound in theproof of the Kadison-Singer conjecture. It applies to product polynomials ofdoubly stochastic matrices through classical results in graph theory due toGodsil, Mohar, Heilmann and Lieb.

  • 966.
    zhong, Liang
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Betting on Volatility: A Delta Hedging Approach2011Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
  • 967. Zhong, Z.
    et al.
    Palenstijn, W. J.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Stockholm, Sweden.
    Batenburg, K. J.
    EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography2018Inngår i: Ultramicroscopy, ISSN 0304-3991, E-ISSN 1879-2723, Vol. 191, s. 34-43Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Energy-dispersive X-ray spectroscopy (EDS) tomography is an advanced technique to characterize compositional information for nanostructures in three dimensions (3D). However, the application is hindered by the poor image quality caused by the low signal-to-noise ratios and the limited number of tilts, which are fundamentally limited by the insufficient number of X-ray counts. In this paper, we explore how to make accurate EDS reconstructions from such data. We propose to augment EDS tomography by joining with it a more accurate high-angle annular dark-field STEM (HAADF-STEM) tomographic reconstruction, for which usually a larger number of tilt images are feasible. This augmentation is realized through total nuclear variation (TNV) regularization, which encourages the joint EDS and HAADF reconstructions to have not only sparse gradients but also common edges and parallel (or antiparallel) gradients. Our experiments show that reconstruction images are more accurate compared to the non-regularized and the total variation regularized reconstructions, even when the number of tilts is small or the X-ray counts are low.

  • 968.
    Zickert, Gustav
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Furstenberg's conjecture and measure rigidity for some classes of non-abelian affine actions on tori2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In 1967 Furstenberg proved that the set {2n3mα(mod 1) | n, m ∈N} is dense in the circle for any irrational α. He also made the following famous measure rigidity conjecture: the only ergodic measures on the circle invariant under both x —> 2x and x —> 3x are the Lebesgue measure and measures supported on a finite set. In this thesis we discuss both Furstenberg’s theorem and his conjecture, as well as the partial solution of the latter given by Rudolph. Following Matheus’presentation of Avila’s ideas for a proof of a weak version of Rudolph’s theorem, we prove a result on extending measure preservation from a semigroup action to a larger semigroup action. Using this result we obtain restrictions on the set of invariant measures for certain classes of non-abelian affine actions on tori. We also study some general properties of affine abelian and non-abelian actions and we show that analogues of Furstenberg’s theorem hold for affine actions on the circle.

  • 969.
    Zickert, Gustav
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Maretzke, Simon
    Univ Gottingen, Inst Numer & Appl Math, Gottingen, Germany..
    Cryogenic electron tomography reconstructions from phaseless data2018Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, nr 12, artikkel-id 124001Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We perform three-dimensional (3D) reconstructions from simulated and real cryogenic electron tomography (cryo-ET) data. Our reconstructions are based on a nonlinear and phaseless forward model very reminiscent of a commonly used model for phase contrast x-ray tomography.

  • 970.
    Ziegenhagen, Stephanie
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    En-cohomology with coefficients as functor cohomology2016Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 16, nr 5, s. 2981-3004Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Building on work of Livernet and Richter, we prove that En -homology and En - cohomology of a commutative algebra with coefficients in a symmetric bimodule can be interpreted as functor homology and cohomology. Furthermore, we show that the associated Yoneda algebra is trivial.

  • 971.
    Öberg, Sebastian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Homotopy Theory and TDA with a View Towards Category Theory2016Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis contains three papers. Paper A and Paper B deal with homotopy theory and Paper C deals with Topological Data Analysis. All three papers are written from a categorical point of view.

    In Paper A we construct categories of short hammocks and show that their weak homotopy type is that of mapping spaces. While doing this we tackle the problem of applying the nerve to large categories without the use of multiple universes. The main tool in showing the connection between hammocks and mapping spaces is the use of homotopy groupoids, homotopy groupoid actions and the homotopy fiber of their corresponding Borel constructions.

    In Paper B we investigate the notion of homotopy commutativity. We show that the fundamental category of a simplicial set is the localization of a subset of the face maps in the corresponding simplex category. This is used to define ∞-homotopy commutative diagrams as functors that send these face maps to weak equivalences. We show that if the simplicial set is the nerve of a small category then such functors are weakly equivalent to functors sending the face maps to isomorphisms. Lastly we show a connection between ∞-homotopy commutative diagrams and mapping spaces of model categories via hammock localization.

    In Paper C we study multidimensional persistence modules via tame functors. By defining noise systems in the category of tame functors we get a pseudo-metric topology on these functors. We show how this pseudo-metric can be used to identify persistent features of compact multidimensional persistence modules. To count such features we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For 1-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction.

  • 972.
    Öberg, Sebastian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Modeling mapping spaces with short hammocks2014Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    We construct a category of short hammocks and show that it has the weak homotopy type of mapping spaces. In doing so we tackle the problem of applying the nerve to large categories without the use of multiple universes. We also explore what the mapping space is. The main tool in showing the connection between hammocks and mapping spaces will be the use of homotopy groupoids, homotopy groupoid actions and the homotopy fiber of their corresponding bar constructions.

  • 973.
    Öberg, Sebastian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Rigidifying homotopy commutative diagramsManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    In this paper we investigate functors indexed by simplex categories that send certain face maps to weak equivalences. We explain why such functors can be regarded as homotopy commutative diagrams. The key question we consider is related to rigidifications of such functors: under what circumstances is such a functor weakly equivalent to a functor that send these face maps to isomorphisms? We show that if the simplicial set is the nerve of a small category then such an homotopy commutative diagram can indeed be rigidified. We conjecture that this is also true whenever the simplicial set is a quasi-category. Lastly we show a connection between our homotopy commutative diagrams and mapping spaces of model categories via hammock localization.

  • 974.
    Öktem, Ozan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Chen, Chong
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Chinese Academy of Sciences, China.
    Onur Domaniç, N.
    Ravikumar, P.
    Bajaj, C.
    Shape-based image reconstruction using linearized deformations2017Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, nr 3, artikkel-id 035004Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce a reconstruction framework that can account for shape related prior information in imaging-related inverse problems. It is a variational scheme that uses a shape functional, whose definition is based on deformable template machinery from computational anatomy. We prove existence and, as a proof of concept, we apply the proposed shape-based reconstruction to 2D tomography with very sparse and/or highly noisy measurements.

  • 975.
    Öktem, Ozan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Pouchol, Camille
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Verdier, O.
    Spatiotemporal PET Reconstruction Using ML-EM with Learned Diffeomorphic Deformation2019Inngår i: 2nd International Workshop on Machine Learning for Medical Image Reconstruction, MLMIR 2019 held in Conjunction with 22nd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2019, Springer, 2019, Vol. 11905, s. 151-162Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Patient movement in emission tomography deteriorates reconstruction quality because of motion blur. Gating the data improves the situation somewhat: each gate contains a movement phase which is approximately stationary. A standard method is to use only the data from a few gates, with little movement between them. However, the corresponding loss of data entails an increase of noise. Motion correction algorithms have been implemented to take into account all the gated data, but they do not scale well in computation time, especially not in 3D. We propose a novel motion correction algorithm which addresses the scalability issue. Our approach is to combine an enhanced ML-EM algorithm with deep learning based movement registration. The training is unsupervised, and with artificial data. We expect this approach to scale very well to higher resolutions and to 3D, as the overall cost of our algorithm is only marginally greater than that of a standard ML-EM algorithm. We show that we can significantly decrease the noise corresponding to a limited number of gates.

  • 976.
    Öktem, Ozan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). KTH, Skolan för teknikvetenskap (SCI), Centra, Strategiskt centrum för industriell och tillämpad matematik, CIAM.
    Quinto, Eric Todd
    Tufts University.
    Skoglund, Ulf
    Okinawa Institute of Science and Technology.
    Electron Lambda-tomography2009Inngår i: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 106, nr 51, s. 21842-21847Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Filtered back-projection and weighted back-projection have long been the methods of choice within the electron microscopy com- munity for reconstructing the structure of macromolecular assem- blies from electron tomography data. Here, we describe electron lambda-tomography, a reconstruction method that enjoys the ben- efits of the above mentioned methods, namely speed and ease of implementation, but also addresses some of their shortcomings. In particular, compared to these standard methods, electron lambda- tomography is less sensitive to artifacts that come from structures outside the region that is being reconstructed, and it can sharpen boundaries.

  • 977.
    Öktem, Ozan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Rullgård, Hans
    Stockholm University.
    Skoglund, Ulf
    Karolinska Institutet.
    A component-wise iterated relative entropy regularization method with updated prior and regularization parameter2007Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 23, nr 5, s. 2121-2139Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a componentwise iterated relative entropy regularization method (COMET) where the prior and regularization parameter could be updated in the iterates. Such a reconstruction method could be useful for multicomponent inverse problems, such as the one occurring in electron tomography. The paper also contains a brief introduction to regularization theory with emphasis on variational based regularization methods, and we rigorously prove that the tolerance-based entropy reconstruction method that occurs in the COMET iterates is a regularization method. We conclude by showing examples of COMET applied to electron tomography data.

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