Sampling at unknown locations, with an application in surface retrieval
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.
Sampling_at_unknown_locations.pdf
postprint
openaccess
CC BY
321.81 KB
Adobe PDF
90b0548d56bc24c295c67fc8d5e96fa0
surface-reconstruction-code_RR.zip
postprint
openaccess
CC BY
288.27 KB
ZIP
f61dcdf795f637b551cd2bef740c4897