2013•arXiv (Cornell University)Open access

Sampling and Reconstruction in Different Subspaces by Using Oblique\n Projections

Peter B. Berger, Karlheinz Gröchenig

Abstract

We introduce a new method for the reconstruction of a function from linear\nmeasurements by means of oblique projections. The space spanned by the\nmeasurement vectors may be different from the subspace in which the function is\nreconstructed. This method is a variation of the generalized sampling of Adcock\nand Hansen. In many cases the use of suitable oblique projections yield a\nbetter quasi-optimality constants than in generalized sampling.\n

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Key concepts: Linear subspace, Oblique case, Oblique projection, Sampling (signal processing), Subspace topology, Mathematics, Function (biology), Space (punctuation)