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Radon transform

About: Radon transform is a(n) research topic. Over the lifetime, 5133 publication(s) have been published within this topic receiving 87244 citation(s). more


Open accessBook
Frank Natterer1Institutions (1)
01 Jan 1986-
Abstract: The Mathematics of Computerized Tomography covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithm, for both standard problems and problems with incomplete data. more

Topics: Reconstruction algorithm (63%), Radon transform (56%), Tomographic reconstruction (55%) more

3,453 Citations

Open accessJournal ArticleDOI: 10.1109/TIP.2002.1014998
Abstract: We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a/spl grave/ trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement. more

Topics: Curvelet (70%), Discrete wavelet transform (66%), Wavelet (64%) more

2,158 Citations

Open accessJournal ArticleDOI: 10.1002/MRM.20279
David S. Tuch1Institutions (1)
Abstract: Magnetic resonance diffusion tensor imaging (DTI) provides a powerful tool for mapping neural histoarchitecture in vivo. However, DTI can only resolve a single fiber orientation within each imaging voxel due to the constraints of the tensor model. For example, DTI cannot resolve fibers crossing, bending, or twisting within an individual voxel. Intravoxel fiber crossing can be resolved using q-space diffusion imaging, but q-space imaging requires large pulsed field gradients and time-intensive sampling. It is also possible to resolve intravoxel fiber crossing using mixture model decomposition of the high angular resolution diffusion imaging (HARDI) signal, but mixture modeling requires a model of the underlying diffusion process. Recently, it has been shown that the HARDI signal can be reconstructed model-independently using a spherical tomographic inversion called the Funk–Radon transform, also known as the spherical Radon transform. The resulting imaging method, termed q-ball imaging, can resolve multiple intravoxel fiber orientations and does not require any assumptions on the diffusion process such as Gaussianity or multi-Gaussianity. The present paper reviews the theory of q-ball imaging and describes a simple linear matrix formulation for the q-ball reconstruction based on spherical radial basis function interpolation. Open aspects of the q-ball reconstruction algorithm are discussed. Magn Reson Med 52:1358–1372, 2004. © 2004 Wiley-Liss, Inc. more

Topics: Tractography (55%), Reconstruction algorithm (54%), Diffusion MRI (54%) more

1,891 Citations

Open accessBook
01 Jul 1983-
Abstract: Providing basic information about the properties of radon transform, this book contains examples and documents a wide variety of applications. It offers guidance to literature related to transform, and is aimed at those with a basic undergraduate background in mathematics. more

Topics: Radon transform (63%), Radon space (57%)

1,837 Citations

Journal ArticleDOI: 10.1364/OL.3.000027
James R. Fienup1Institutions (1)
01 Jul 1978-Optics Letters
Abstract: We present a digital method for solving the phase-retrieval problem of optical-coherence theory: the reconstruction of a general object from the modulus of its Fourier transform. This technique should be useful for obtaining high-resolution imagery from interferometer data. more

1,559 Citations

No. of papers in the topic in previous years

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Topic's top 5 most impactful authors

Boris Rubin

29 papers, 486 citations

Mai K. Nguyen

23 papers, 294 citations

Markus Haltmeier

21 papers, 743 citations

Eric Todd Quinto

21 papers, 603 citations

Sunghwan Moon

19 papers, 130 citations

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