Total variation based interpolation

We propose an reversible interpolation method for signals or images, in the sense that the original image can be deduced from its interpolation by a sub-sampling. This imposes some constraints on the Fourier coefficients of the interpolated image. Now, there still exist many possible interpolations that satisfy these constraints. The zero-padding method is one of them, but gives very oscillatory images. We propose to choose among all possibilities, the one which is the most "regular". We justify the total variation of the image as a good candidate as measure of regularity. This yields to minimise a regularisation functional defined in space domain, with a constraint defined in the frequency domain.