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New generations of complex and steerable wavelets – Application to noise reduction in MRI

Jesse Berent

Section Microtechnique, EPFL

Diploma Project
June 2004

In this paper, we present a short overview of different complex and directional wavelet transforms developed. We then evaluate their denoising performances with synthetic MRI images containing additive Gaussian white noise in their real and imaginary parts. The complex wavelets approached are the complex Daubechies, complex fractional splines, complex rotation covariant wavelets and the complex dual-tree transform. The real-valued steerable pyramid is also compared. Additionally, we provide a Matlab toolbox gathering all the functions necessary for 1D and 2D signal analysis with the wavelet transforms mentioned above. An extensive graphic interface is also made available for the wavelet decompositions and denoising by means of thresholding.