Problema de tomografía local usando wavelets B-spline cúbicos

Local tomography problem using cubic B-spline wavelets

  • Wilmar Alberto Díaz Ossa Universidad Distrital Francisco José de Caldas
  • Harold Vacca González Universidad Distrital Francisco José de Caldas

Resumen (es_ES)

En el presente artículo se describe e implementa una solución al problema de la tomografía local, equivalente a la inversión de la transformada de Radon, utilizando la transformada wavelet. Para ello se ejecuta un algoritmo basado en wavelets B-spline cúbicos de soporte compacto con suficientes momentos de desvanecimiento para que la función de escalado filtrada, la wavelet madre y su transformada de Hilbert tengan decaimiento rápido. Lo anterior favorece la localización de la transformada wavelet de la transformada de Radon y, por tanto, la inversión, es decir; la reconstrucción de una región central de interés del fantasma Shepp-Logan.

Resumen (en_US)

This paper presents a formal description and subsequent implementation of a solution to the local tomography problem, equivalent to the so-called Radon Transform local Inversion. To do so, it is necessary to execute an algorithm based on compact-support B-spline cubic wavelets, including sufficient vanishing moments so that the filtered-scaling, the mother wavelet and its Hilbert Transform functions decay rapidly. This favors localization of Radon-Transform Wavelet Transform and, therefore, its corresponding inversion; that is, the reconstruction of a Shepp-Logan Phantom central interest region (ROI).

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Biografía del autor/a

Wilmar Alberto Díaz Ossa, Universidad Distrital Francisco José de Caldas
Licenciado en matemáticas, Universidad Pedagógica Nacional; magíster en matemáticas aplicadas, Universidad EAFIT. Docente de la Universidad Distrital Francisco José de Caldas, Bogotá.
Harold Vacca González, Universidad Distrital Francisco José de Caldas

Licenciado en matemáticas, Universidad Distrital Francisco José de Caldas; magíster en matemáticas aplicadas, Universidad EAFIT. Docente de la Universidad Distrital Francisco José de Caldas, Bogotá.

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Cómo citar
Díaz Ossa, W. A., & Vacca González, H. (2014). Problema de tomografía local usando wavelets B-spline cúbicos. Tecnura, 18, 13-30. https://doi.org/10.14483/udistrital.jour.tecnura.2014.SE1.a01
Publicado: 2014-12-01
Sección
Investigación