Radon-Nikodym approximation in application to image analysis

Understand

For an image pixel information can be converted to the moments of some basis $Q_k$, e.g.

• Fourier-Mellin, Zernike, monomials, etc.
• Given sufficient number of moments pixel information can be completely recovered, for insufficient number of moments only partial information can be recovered and the image reconstruction is, at best, of interpolatory type.
• Standard approach is to present interpolated value as a linear combination of basis functions, what is equivalent to least squares expansion.