In this work we propose the use of B-spline functions for the parametric representation of high resolution images from low sampled data in the Fourier domain. Traditionally, exponential basis functions are employed in this situation, but they produce artifacts and amplify the noise on the data. We present the method in an algorithmic form and carefully consider the problem of solving the ill-conditioned linear system arising from the method by an e±cient regularization method. Two applications of the proposed method to dynamic Magnetic Resonance images are considered. Dynamic Magnetic Resonance acquires a time series of images of the same slice of the body; in order to fasten the acquisition, the data are low sampled in the Fourier space. Numerical experiments have been performed both on simulated and real Magnetic Resonance data. They show that the B-splines reduce the artifacts and the noise in the representation of high resolution MR images from low sampled data

Representation of high resolution images from low sampled Fourier data. Applications to dynamic MRI / G. landi; E. Loli Piccolomini. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 26:(2006), pp. 27-40. [10.1007/s10851-006-7617-4]

Representation of high resolution images from low sampled Fourier data. Applications to dynamic MRI.

LANDI, GERMANA;LOLI PICCOLOMINI, ELENA
2006

Abstract

In this work we propose the use of B-spline functions for the parametric representation of high resolution images from low sampled data in the Fourier domain. Traditionally, exponential basis functions are employed in this situation, but they produce artifacts and amplify the noise on the data. We present the method in an algorithmic form and carefully consider the problem of solving the ill-conditioned linear system arising from the method by an e±cient regularization method. Two applications of the proposed method to dynamic Magnetic Resonance images are considered. Dynamic Magnetic Resonance acquires a time series of images of the same slice of the body; in order to fasten the acquisition, the data are low sampled in the Fourier space. Numerical experiments have been performed both on simulated and real Magnetic Resonance data. They show that the B-splines reduce the artifacts and the noise in the representation of high resolution MR images from low sampled data
2006
Representation of high resolution images from low sampled Fourier data. Applications to dynamic MRI / G. landi; E. Loli Piccolomini. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 26:(2006), pp. 27-40. [10.1007/s10851-006-7617-4]
G. landi; E. Loli Piccolomini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/43791
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