Application of the discrete torus wavelet transform to the denoising of magnetic resonance images of uterine and ovarian masses

Gordon E. Sarty; M. Stella Atkins; Femi Olatunbosun; Donna Chizen; John Loewy; Edward J. Kendall; Roger A. Pierson

doi:10.1117/12.366816

26 October 1999 Application of the discrete torus wavelet transform to the denoising of magnetic resonance images of uterine and ovarian masses

Gordon E. Sarty, M. Stella Atkins, Femi Olatunbosun, Donna Chizen, John Loewy, Edward J. Kendall, Roger A. Pierson

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Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366816
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

A new numerical wavelet transform, the discrete torus wavelet transform, is described and an application is given to the denoising of abdominal magnetic resonance imaging (MRI) data. The discrete tori wavelet transform is an undecimated wavelet transform which is computed using a discrete Fourier transform and multiplication instead of by direct convolution in the image domain. This approach leads to a decomposition of the image onto frames in the space of square summable functions on the discrete torus, l²(T²). The new transform was compared to the traditional decimated wavelet transform in its ability to denoise MRI data. By using denoised images as the basis for the computation of a nuclear magnetic resonance spin-spin relaxation-time map through least squares curve fitting, an error map was generated that was used to assess the performance of the denoising algorithms. The discrete torus wavelet transform outperformed the traditional wavelet transform in 88% of the T₂ error map denoising tests with phantoms and gynecologic MRI images.

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Gordon E. Sarty, M. Stella Atkins, Femi Olatunbosun, Donna Chizen, John Loewy, Edward J. Kendall, and Roger A. Pierson "Application of the discrete torus wavelet transform to the denoising of magnetic resonance images of uterine and ovarian masses", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366816

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KEYWORDS

Wavelet transforms

Denoising

Magnetic resonance imaging

Wavelets

Signal to noise ratio

Interference (communication)

Magnetism

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