On interpolation of differentially structured images

A vector space approach to image reconstruction is derived and introduced. The continuous-domain image is assumed to belong to a reproducing kernel Hilbert space and the sampling process is shown to correspond to an appropriate orthogonal projection. The values at the interpolating grid are shown to correspond to a set of inner product calculations, giving rise to a minimax solution for an ℓ₂ approximation problem. A tight upper bound on the ensued error is then derived and demonstrated. Examples of image resizing show that the proposed method yields better results than presently available methods, including the cubic B-spline method, in terms of SNR.