Sökning: "Radon transform"

Visar resultat 1 - 5 av 10 avhandlingar innehållade orden Radon transform.

  1. 1. Studies of vector tomography

    Författare :Kent Stråhlén; Matematik LTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Doppler tomography; Doppler Radon transform; local tomography; vectorial k-plane transform; vectorial Radon transform; k-plane transform; Radon transform; tomography; vector tomography; Mathematics; Matematik;

    Sammanfattning : The motivation to study the kind of problems appearing in this thesis has been ultrasound measurements of flows, from which velocity spectra along lines can be determined. These velocity spectra can mathematically be described by a new non-linear transform, here called the Doppler Spectral Transform (DST). LÄS MER

  3. 2. On Invertibility of the Radon Transform and Compressive Sensing

    Författare :Joel Andersson; Jan-Olov Strömberg; Mikko Salo; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Radon transform; invertibility; compressive sensing; stability estimates; Mathematics; Matematik;

    Sammanfattning : This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals. LÄS MER

  4. 3. Fast Radon Transforms and Reconstruction Techniques in Seismology

    Författare :Viktor Nikitin; Matematik LTH; []
    Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Fourier transform FFT ; Radon transforms; GPU;

    Sammanfattning : The measurements conducted in tomography and seismology typically yield large multidimensional data sets. This in combination with the fact that the data may have an irregular structure makes it computationally prohibitive to use simple reconstruction methods directly. LÄS MER

  5. 4. Inverse Problems in Tomography and Fast Methods for Singular Convolutions

    Författare :Fredrik Andersson; Matematik LTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik; Unequally spaced FFT; Integral transforms; Singular integrals; Lippmann?Schwinger equation; Helmholtz equation; Inverse problems; Fast Gauss transform; Fast summation; Convolution; Radon transform; Tomography;

    Sammanfattning : There are two, partially interlaced, themes treated in this thesis; inverse problems of tomographic type and fast and accurate methods for the application of convolution operators. Regarding the first theme, the inverse problem of Doppler tomography is considered and the Doppler moment transform is introduced for that purpose. LÄS MER

  7. 5. Extension of separately analytic functions and applications to mathematical tomography : characterizing the range of the exponential Radon transform

    Författare :Ozan Öktem; Slawomir Kolodziej; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; matematik; Mathematics;

    Sammanfattning : The principal problem that is dealt with in the thesis is to characterize the range of the exponential Radon transform for both constant attenuation and angle dependent attenuation (in the latter case we assume that the attenuation is a trigonometric polynomial). Such results are also of interest in applications such as ECT (Emission Computed Tomography). LÄS MER