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  • 2551.
    Åström, Freddie
    Linköpings universitet, Institutionen för systemteknik, Datorseende. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska högskolan.
    Variational Tensor-Based Models for Image Diffusion in Non-Linear Domains2015Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    This dissertation addresses the problem of adaptive image filtering.

    Although the topic has a long history in the image processing community, researchers continuously present novel methods to obtain ever better image restoration results.

    With an expanding market for individuals who wish to share their everyday life on social media, imaging techniques such as compact cameras and smart phones are important factors. Naturally, every producer of imaging equipment desires to exploit cheap camera components while supplying high quality images. One step in this pipeline is to use sophisticated imaging software including, e.g., noise reduction to reduce manufacturing costs, while maintaining image quality.

    This thesis is based on traditional formulations such as isotropic and tensor-based anisotropic diffusion for image denoising. The difference from main-stream denoising methods is that this thesis explores the effects of introducing contextual information as prior knowledge for image denoising into the filtering schemes. To achieve this, the adaptive filtering theory is formulated from an energy minimization standpoint. The core contributions of this work is the introduction of a novel tensor-based functional which unifies and generalises standard diffusion methods. Additionally, the explicit Euler-Lagrange equation is derived which, if solved, yield the stationary point for the minimization problem. Several aspects of the functional are presented in detail which include, but are not limited to, tensor symmetry constraints and convexity. Also, the classical problem of finding a variational formulation to a given tensor-based partial differential equation is studied.

    The presented framework is applied in problem formulation that includes non-linear domain transformation, e.g., visualization of medical images.

    Additionally, the framework is also used to exploit locally estimated probability density functions or the channel representation to drive the filtering process.

    Furthermore, one of the first truly tensor-based formulations of total variation is presented. The key to the formulation is the gradient energy tensor, which does not require spatial regularization of its tensor components. It is shown empirically in several computer vision applications, such as corner detection and optical flow, that the gradient energy tensor is a viable replacement for the commonly used structure tensor. Moreover, the gradient energy tensor is used in the traditional tensor-based anisotropic diffusion scheme. This approach results in significant improvements in computational speed when the scheme is implemented on a graphical processing unit compared to using the commonly used structure tensor.

  • 2552.
    Åström, Kalle
    et al.
    Centre for Mathematical Sciences, Lund University.
    Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Silvestrov, Sergei D.Division of Applied Mathematics, Mälardalen University.
    Analysis for science, engineering and beyond: the tribute workshop in honour of Gunnar Sparr held in Lund, May 8-9, 20082012Collection/Antologi (Annet vitenskapelig)
  • 2553.
    Åström, Karl
    et al.
    Lund university.
    Persson, Lars-ErikLuleå university.Silvestrov, SergeiMälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Analysis for Science, Engineering and Beyond The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 20082012Collection/Antologi (Fagfellevurdert)
  • 2554.
    Öberg, Anders
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Algorithms for approximation of invariant measures for IFS2005Inngår i: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 116, nr 1, s. 31-55Artikkel i tidsskrift (Fagfellevurdert)
  • 2555.
    Öberg, Anders
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematik I-5.
    Approximation of invariant measures for random iterations2006Inngår i: Rocky Mountain Journal of Mathematics, ISSN 0035-7596, E-ISSN 1945-3795, Vol. 36, nr 1, s. 273-301Artikkel i tidsskrift (Fagfellevurdert)
  • 2556.
    Öberg, Anders
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematik I-5.
    Strichartz, Robert S.
    Yingst, Andrew Q.
    Level sets of harmonic functions on the Sierpinski gasket2002Inngår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 40, nr 2, s. 335-362Artikkel i tidsskrift (Fagfellevurdert)
  • 2557.
    Ödling, Per
    et al.
    Luleå tekniska universitet.
    Koski, Timo
    Luleå tekniska universitet.
    Börjesson, Per Ola
    Luleå tekniska universitet.
    A reduced complexity viterbi equalizer used in conjunction with a pulse shaping method1992Inngår i: Proceedings of Nordic Radio Symposium: NRS 92 : wave propagation, personal, mobile and satellite communications / in co-operation with AUC - Aalborg University / [ed] Chr. Christensen, Aalborg: Aalborg University , 1992, s. 91-94Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The complexity of the Viterbi algorithm can be reduced by linear pre-equalization. We introduce a linear preprocessor using the weighted least squares filtering of [10]. The geometric technique of L.Barbosa [3] is evoked for analytical representation of the complexity reduction by pre-equalization, and for evaluation of error performance. We give results on the bit error rate of the WLS preprocessor and of the linear preprocessor of Falconer and Magee [6].

  • 2558.
    Öhman, Eric
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Analys av bostadsrättspriser medmultipel linjär regression ochprissättning i praktiken2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med denna rapport är att undersöka de faktorer som påverkar priset på bostadsrätter i Stockholms innerstad och hur mycket dessa faktorer påverkar priset med multipel linjär regression.  Resultaten från regressionsanalysen används för att skapa en modell för att prissätta bostadsrätter i Stockholms innerstad.  Denna modell jämförs med de metoder som byggnationsföretag vars verksamhet riktar sig mot försäljning av nybyggda bostadsrätter direkt till kund för att se om de metoder som används idag går att förbättra.  Arbetet resulterade i en modell som kan ge en indikation på hur mycket olika faktorer påverkar priset samt en grund för bostadsrättsvärdering i Stockholms innerstad.  De metoder som används idag visade sig inte kunna förbättras med de resultat som togs fram i denna rapport då fördelarna med dessa metoder är dess anpassningsbarhet efter ett projekts unika egenskaper samt avgränsningar till relevanta marknader.

  • 2559.
    Öktem, Ozan
    Sidec, Kista, Sweden.
    Reconstruction methods in electron tomography2008Inngår i: Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT) / [ed] Y. Censor, Jiang M., and Louis A. K., Springer Berlin/Heidelberg, 2008, s. 289-320Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Already in 1968 one recognized that the transmission electron micro- scope could be used in a tomographic setting as a tool for structure determination of macromolecules. However, its usage in mainstream structural biology has been limited and one reason is the devastating combination of noisy data and incomplete data problems that leads to severe ill-posedness of the inverse problem. Despite these issues, the importance of electron tomography is beginning to increase, espe- cially in drug discovery. This review begins with a brief introduction to the model for image formation, i.e. the forward operator. Next, we state the difficulties and review some of the various attempts at overcoming those in solving the inverse problem.

  • 2560.
    Öktem, Ozan
    et al.
    Sidec AB, Kista, Sweden.
    Fanelli, Duccio
    University of Florens.
    Electron tomography: A short overview with an emphasis on the absorption potential model for the forward problem2008Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 24, nr 1, s. 013001-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This review of the development and current status of electron tomography deals mainly with the mathematical and algorithmic aspects. After a very brief description of the role of electron tomography in structural biology, we turn our attention to the derivation of the forward operator. Starting from the Schrodinger equation, the electron - specimen interaction is modelled as a diffraction tomography problem and the picture is completed by adding a description of the optical system of the transmission electron microscope. The first- order Born approximation enables one to explicitly express the intensity for any finite wavenumber in terms of the propagation operator acting on the specimen convolved with a point spread function, derived from the optics in the transmission electron microscope. Next, we focus on the difficulties that cause the reconstruction problem to be quite challenging. Special emphasis is put on explaining the extremely low signal- to- noise ratio in the data combined with the incomplete data problems, which lead to severe ill- posedness. The next step is to derive the standard phase contrast model used in the electron tomography community. The above- mentioned expression for the intensity generalizes the standard phase contrast model which can be obtained by replacing the propagation operator by its high- energy limit, the x- ray transform, as the wavenumber tends to infinity. The importance of more carefully including the wave nature of the electron - specimen interaction is supported by performing an asymptotic analysis of the intensity as the wavenumber tends to infinity. Next we provide an overview of the various reconstruction methods that have been employed in electron tomography and we conclude by mentioning a number of open problems. Besides providing an introduction to electron tomography written in the 'language of inverse problems', the authors hope to raise interest among experts in integral geometry and regularization theory for the mathematical and algorithmic difficulties that are encountered in electron tomography.

  • 2561.
    Öktem, Ozan
    et al.
    Sidec, Kista, Sweden.
    Quinto, Eric Todd
    Tufts University.
    Inversion of the X-ray transform from limited angle parallel beam region of interest data with applications to electron tomography2007Inngår i: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 7, nr 1, s. 1050301-1050302Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a new local tomographic algorithm applicable to electron microscopy tomography. Our algorithm applies to the standard data acquisition method, single-axis tilting, as well as for more arbitrary acquisition methods. Using microlocal analysis we put the reconstructions in a mathematical context, explaining which singularities are stably visible from the limited data given by the data collection protocol in the electron microscope.

  • 2562.
    Öktem, Ozan
    et al.
    Sidec Technologies, Kista, Sweden.
    Quinto, Eric Todd
    Tufts University.
    Local tomography in electron microscopy2008Inngår i: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 68, nr 5, s. 1282-1303Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a new local tomographic algorithm applicable to electron microscope tomography. Our algorithm applies to the standard data acquisition method, single-axis tilting, as well as to more arbitrary acquisition methods including double axis and conical tilt. Using microlocal analysis we put the reconstructions in a mathematical context, explaining which singularities are stably visible from the limited data given by the data collection protocol in the electron microscope. Finally, we provide reconstructions of real specimens from electron tomography data.

  • 2563.
    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.

  • 2564.
    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.

  • 2565. Agarwal, R.P.
    Persson, Lars-Erik
    Zafer, A.
    Selected papers of the international workshop on difference and differential inequalities, Gebze, Kocaeli, Turkey, July 3--7, 19961998Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, nr 3, s. 347-461Artikkel i tidsskrift (Fagfellevurdert)
49505152 2551 - 2565 of 2565
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