Reconstruction of Multidimensional Signals from Irregular Noisy Samples

Details Reconstruction of Multidimensional Signals from Irregular Noisy Samples Reconstruction of Multidimensional Signals from Irregular Noisy Samples

2008-04-21

arxiv.org/abs/0804.3255v1

Computer Science

Information Theory

To appear on IEEE Transactions on Signal Processing, 2008

Scientific paper

10.1109/TSP.2008.925953

We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More specifically, we apply linear reconstruction techniques and take the mean square error (MSE) of the field estimate as a metric to evaluate the signal reconstruction quality. We find that the MSE analysis could be carried out by using the closed-form expression of the eigenvalue distribution of the matrix representing the sampling system. Unfortunately, such distribution is still unknown. Thus, we first derive a closed-form expression of the distribution moments, and we find that the eigenvalue distribution tends to the Marcenko-Pastur distribution as the field dimension goes to infinity. Finally, by using our approach, we derive a tight approximation to the MSE of the reconstructed field.

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