Multi-scale transforms have got a lot of applications in image
processing, in recent years. Wavelet transform is a powerful
multiscale transform for denoising noisy signals and images, but
the usual two-dimensional separable wavelets are sub-optimal.
These separable wavelet transforms can successfully identify zero
dimensional singularities in images, but can weakly identify one
dimensional singularities such as edges, curves and lines. In
this sense, non-separable transforms such as Ridgelet and
Curvelet transforms are proposed by Candes and Donoho. The
coefficients produced by these non-separable transforms have
shown to be sparser than wavelet coefficients. This fact results
in better denoising capabilities than wavelet transform. These
new non-separable transforms can identify direction in lines and
curves, because of special structure of their basis elements.
Basically, Magnetic Resonance images are probable to have Rician
noise. In some special cases, this kind of noise can be supposed
to be white Gaussian noise. In this paper, a new method for
denoising MR images is proposed. This method is based on
Monoscale Ridgelet transform. It is shown that this two transform can successfully denoise MR images embedded in white Gaussian noise. The results are better in comparison with usual wavelet denoising methods, based on both visual perception and signal-to-noise ratio.