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We introduce a continuous domain framework for the recovery of points on asurface in high dimensional space, represented as the zero-level set of abandlimited function. We show that the exponential maps of the points on thesurface satisfy annihilation relations, implying that they lie in a finitedimensional subspace. The subspace properties are used to derive samplingconditions, which will guarantee the perfect recovery of the surface fromfinite number of points. We rely on nuclear norm minimization to exploit thelow-rank structure of the maps to recover the points from noisy measurements.Since the direct estimation of the surface is computationally prohibitive invery high dimensions, we propose an iterative reweighted algorithm using the"kernel trick". The iterative algorithm reveals deep links to Laplacian basedalgorithms widely used in graph signal processing; the theory and the samplingconditions can serve as a basis for discrete-continuous domain processing ofsignals on a graph.

Recovery of Noisy Points on Band-limited Surfaces: Kernel Methods Re-explained