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Robust Multidimentional Chinese Remainder Theorem for Integer Vector Reconstruction
The problem of robustly reconstructing an integer vector from its erroneous
remainders appears in many applications in the field of multidimensional (MD)
signal processing. To address this problem, a robust MD Chinese remainder
theorem (CRT) was recently proposed for a special class of moduli, where the
remaining integer matrices left-divided by a greatest common left divisor
(gcld) of all the moduli are pairwise commutative and coprime. The strict
constraint on the moduli limits the usefulness of the robust MD-CRT in
practice. In this paper, we investigate the robust MD-CRT for a general set of
moduli. We first introduce a necessary and sufficient condition on the
difference between paired remainder errors, followed by a simple sufficient
condition on the remainder error bound, for the robust MD-CRT for general
moduli, where the conditions are associated with (the minimum distances of)
these lattices generated by gcld's of paired moduli, and a closed-form
reconstruction algorithm is presented. We then generalize the above results of
the robust MD-CRT from integer vectors/matrices to real ones. Finally, we
validate the robust MD-CRT for general moduli by employing numerical
simulations, and apply it to MD sinusoidal frequency estimation based on
multiple sub-Nyquist samplers.Comment: 12 pages, 5 figur
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