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Generalized Sampling and Constrained Landmark Interpolation

M. Unser

Proceedings of the First 2002 SIAM Conference on Imaging Science (SIAG-IS'02), Boston MA, USA, March 4-6, 2002, Session MS17, pp. 45.



We present a general approach to generalized sampling and signal reconstruction in a variational framework. We consider measurements that are the non-uniform samples of a signal and/or some filtered versions of it. We define a general class of quadratic plausibility criteria (regularization term) which are specified in the continuous domain. The reconstruction is then a function minimizing the plausibility criterion under the consistency constraints. Alternatively, the consistency error (not necessarily quadratic) can be also bound by an a priori limit. We prove that, in both cases, the solution can be expressed as a linear combination of continuously-defined basis functions which have a translation-invariant structure. In the quadratic case, the problem then boils down to the resolution of a linear set of equations.

We present an application of this theory to landmark registration with additional constraints on the gradient of the deformation field. We justify the choice of the plausibility criterion given the general properties we want the solution to have.


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