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The problem of robustly reconstructing an integer vector from its erroneousremainders appears in many applications in the field of multidimensional (MD)signal processing. To address this problem, a robust MD Chinese remaindertheorem (CRT) was recently proposed for a special class of moduli, where theremaining integer matrices left-divided by a greatest common left divisor(gcld) of all the moduli are pairwise commutative and coprime. The strictconstraint on the moduli limits the usefulness of the robust MD-CRT inpractice. In this paper, we investigate the robust MD-CRT for a general set ofmoduli. We first introduce a necessary and sufficient condition on thedifference between paired remainder errors, followed by a simple sufficientcondition on the remainder error bound, for the robust MD-CRT for generalmoduli, where the conditions are associated with (the minimum distances of)these lattices generated by gcld's of paired moduli, and a closed-formreconstruction algorithm is presented. We then generalize the above results ofthe robust MD-CRT from integer vectors/matrices to real ones. Finally, wevalidate the robust MD-CRT for general moduli by employing numericalsimulations, and apply it to MD sinusoidal frequency estimation based onmultiple sub-Nyquist samplers.

Robust Multidimentional Chinese Remainder Theorem for Integer Vector Reconstruction