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Sampling multidimensional signals by a new class of quasi-random sequences

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Abstract

A new method of equidistributed (EQD) sampling of nD signals is proposed and investigated. Equidistributed or quasi-random (QR) sequences are deterministic sequences, which cover nD space more evenly than uniformly distributed random sequences. We propose to generate quasi-random nD sample sites using space-filling curves, which propagate their measure and neighborhood preserving properties to sample points. It is proved that these points are not only equidistributed but also well distributed, which results in a good volume approximation from samples of 2D and 3D images. A general way of reconstructing output of a linear system from QR samples of its input nD signals is also proposed and proved to be convergent. As an example of applications of the theory, a double radial basis neural network is proposed, which allows for the reconstruction of 2D cross-sections from samples of 3D image or from a video sequence of 2D images.

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Authors and Affiliations

  1. Wroclaw University of Technology, Institute of Computer Eng., Control and Robotics, Wyb. Wyspianskiego 27, 50 370, Wroclaw, Poland

    Ewa Skublska-Rafajłowicz & Ewaryst Rafajłowicz

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  1. Ewa Skublska-Rafajłowicz
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  2. Ewaryst Rafajłowicz
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Correspondence to Ewaryst Rafajłowicz.

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Skublska-Rafajłowicz, E., Rafajłowicz, E. Sampling multidimensional signals by a new class of quasi-random sequences. Multidim Syst Sign Process 23, 237–253 (2012). https://doi.org/10.1007/s11045-010-0120-5

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  • DOI: https://doi.org/10.1007/s11045-010-0120-5

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