  Mathematical methods of image inpainting involve the discretization of given
continuous models. We present a method that avoids the standard pointwise
discretization by modeling known variational approaches, in particular total
variation (TV), using a finite dimensional spline space. Besides the analysis
of the resulting model, we present a numerical implementation based on the
alternating method of multipliers. We compare the results numerically with
classical TV inpainting and give examples of applications.
