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

2013/12/06 by Peter Berger, Karlheinz Gröchenig, Berger, Peter +2
Decision Sciences · Engineering · Mathematics · #42C15 #Advanced Measurement and Metrology Techniques #Control Systems and Identification #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Scientific Measurement and Uncertainty Evaluation

paper · pdf · doi:10.48550/arxiv.1312.1717

openalex publication_date 2013/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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