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

摘要

Abstract: A new numerical wavelet transform, the discrete toruswavelet transform, is described and an application isgiven to the denoising of abdominal magnetic resonanceimaging (MRI) data. The discrete tori wavelet transformis an undecimated wavelet transform which is computedusing a discrete Fourier transform and multiplicationinstead of by direct convolution in the image domain.This approach leads to a decomposition of the imageonto frames in the space of square summable functionson the discrete torus, l$+2$/(T$+2$/). The newtransform was compared to the traditional decimatedwavelet transform in its ability to denoise MRI data.By using denoised images as the basis for thecomputation of a nuclear magnetic resonance spin-spinrelaxation-time map through least squares curvefitting, an error map was generated that was used toassess the performance of the denoising algorithms. Thediscrete torus wavelet transform outperformed thetraditional wavelet transform in 88% of the T$-2$/error map denoising tests with phantoms and gynecologicMRI images.!10