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  • 1. Chen, C.
    et al.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Indirect image registration with large diffeomorphic deformations2018In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 11, no 1, p. 575-617Article in journal (Refereed)
    Abstract [en]

    This paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting, where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends to zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data. 

  • 2.
    Hamid Muhammed, Hamed
    et al.
    KTH, School of Technology and Health (STH), Medical Engineering.
    Bergholm, Fredrik
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Sensitivity Analysis of Multichannel Images Intended for Instantaneous Imaging Spectrometry Applications2010In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 3, no 1, p. 79-109Article in journal (Refereed)
    Abstract [en]

    This paper presents a sensitivity analysis of using instantaneous multichannel two-dimensional (2D) imaging to achieve instantaneous 2D imaging spectroscopy. A simulated multiple-filter mosaic was introduced and used to acquire multichannel data which were transformed into spectra. The feasibility of two different transformation approaches (the concrete pseudoinverse approach and a statistical approach) was investigated through extensive experimental tasks. A promising statistical method was identified to be used for accurate estimation of spectra from multichannel data. Comparison between estimated and measured spectra shows that higher estimation accuracy can be achieved when using a larger number of usable multiple-filter combinations in the mosaic.

  • 3.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport2017In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 10, no 4, p. 1935-1962Article in journal (Refereed)
    Abstract [en]

    The optimal mass transport problem gives a geometric framework for optimal allocation and has recently attracted significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be formulated as a linear programming problem, it is in many cases intractable for large problems due to the vast number of variables. A recent development addressing this builds on an approximation with an entropic barrier term and solves the resulting optimization problem using Sinkhorn iterations. In this work we extend this methodology to a class of inverse problems. In particular we show that Sinkhorn-type iterations can be used to compute the proximal operator of the transport problem for large problems. A splitting framework is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate this method on problems in computerized tomography. In particular we consider a limited-angle computerized tomography problem, where a priori information is used to compensate for missing measurements.

  • 4.
    Lindeberg, Tony
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Dense scale selection over space, time and space-time2018In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 11, no 1, p. 407-441Article in journal (Refereed)
    Abstract [en]

    Scale selection methods based on local extrema over scale of scale-normalized derivatives have been primarily developed to be applied sparsely---at image points where the magnitude of a scale-normalized differential expression additionally assumes local extrema over the domain where the data are defined. This paper presents a methodology for performing dense scale selection, so that hypotheses about local characteristic scales in images, temporal signals, and video can be computed at every image point and every time moment. A critical problem when designing mechanisms for dense scale selection is that the scale at which scale-normalized differential entities assume local extrema over scale can be strongly dependent on the local order of the locally dominant differential structure. To address this problem, we propose a methodology where local extrema over scale are detected of a quasi quadrature measure involving scale-space derivatives up to order two and propose two independent mechanisms to reduce the phase dependency of the local scale estimates by (i) introducing a second layer of postsmoothing prior to the detection of local extrema over scale, and (ii) performing local phase compensation based on a model of the phase dependency of the local scale estimates depending on the relative strengths between first- and second-order differential structures. This general methodology is applied over three types of domains: (i) spatial images, (ii) temporal signals, and (iii) spatio-temporal video. Experiments demonstrate that the proposed methodology leads to intuitively reasonable results with local scale estimates that reflect variations in the characteristic scales of locally dominant structures over space and time.

  • 5.
    Niinimäki, Kati
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lassas, Matti
    Hamalainen, Keijo
    Kallonen, Aki
    Kolehmainen, Ville
    Niemi, Esa
    Siltanen, Samuli
    Multiresolution Parameter Choice Method for Total Variation Regularized Tomography2016In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 9, no 3, p. 938-974Article in journal (Refereed)
    Abstract [en]

    A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. A partial understanding of the properties of the method is provided by rigorously proving that the TV norms of the reconstructions converge with any choice of regularization parameter. The computational approach is based on computing reconstructions at a few different resolutions and various values of regularization parameter. The chosen parameter is the smallest one resulting in approximately discretization-invariant TV norms of the reconstructions. The method is tested with simulated and experimental X-ray tomography data and compared to the S-curve method. The results are comparable to those of the S-curve method. However, the S-curve method needs quantitative a priori information about the expected sparsity (TV norm) of the unknown, while the proposed method does not require such input parameters.

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