Interpolation with non-ideal sampling compensation

Abstract

According to general sampling theory, a signal f may be rebuilt from its sampled version, given a non-ideal analysis function (e.g. device impulse response). Reconstruction is done by convolution with a digital correction filter q, followed by interpolation by a synthesis function. The solution for q, whose finding is the challenge, has to guarantee a consistency constraint, which makes the system equivalent for the signal to a projection operator.

In the frame of this project, solutions for q are extended especially for the 2D case. A signal extrapolation system (for both 1D and 2D cases), in which an upsampling by two step precedes q filtering, is treated ; since degrees of freedom appear, regularization (which is chosen to be minimization of the laplacian energy, for the 2D case) is used as an additional condition to guarantee the stability and uniqueness of the solution for the filter q.

Theoretical solutions are implemented in Java, in form of an image processing plugin for ImageJ.

Start, sampled (analysis : dilated rect) and reconstructed (synthesis : cubic B-Spline) images