Wavelet Enhancement of an MRI Image

As an example of accessing the properties of a two-dimensional image at different resolutions, we consider a medical MRI image of a person's head. The data is contained in the variable MRIdata.

Show MRI Image

We use a fourth order least asymmetric filter to perform a wavelet transform of this image.

\(s4 = LeastAsymmetricFilter[4]; 

    wtdata = WaveletTransform[MRIdata, s4, 4, 
        BoundaryCondition -> Fixed]; \)

These three images show the details at level 4.  Each of the three two-dimensional mother wavelets is sensitive to different aspects of the details at a given level.

Show Level 4 Wavelet Detail

The wavelet coefficients are surpressed by  90% for all levels except those at the finest level of resolution. We then perform the inverse wavelet transformation and show the image.  This effectively enhances the details in the original image while retaining some information at all levels as a reference.

Enhance MRI Image

Show[GraphicsArray[{originalImage, enhancedImage}]];