Sampling at unknown locations, with an application in surface retrieval
Autor: | Martin Vetterli, Michalina Pacholska, Benjamin Bejar Haro, Adam Scholefield |
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Rok vydání: | 2017 |
Předmět: |
Surface (mathematics)
Polynomial Iterative method Mathematical analysis Sampling (statistics) 020206 networking & telecommunications 02 engineering and technology Function (mathematics) Rational function 010501 environmental sciences 01 natural sciences Arbitrarily large 0202 electrical engineering electronic engineering information engineering Uniqueness Algorithm 0105 earth and related environmental sciences Mathematics |
Zdroj: | 2017 International Conference on Sampling Theory and Applications (SampTA). |
Popis: | We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from the original, that could have generated the same samples. In other words, the error can be arbitrarily large. Motivated by this, we prove that, for polynomials, if the sample positions are constrained such that they can be described by an unknown rational function, uniqueness can be achieved. In addition to our theoretical results, we show that, in 1-D, the problem of recovering a painted surface from a single image exactly fits this framework. Furthermore, we propose a simple iterative algorithm for recovering both the surface and the texture and test it with simple simulations. |
Databáze: | OpenAIRE |
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