2008/04/21 by Alessandro Nordio, A. Nordio, Carla Fabiana Chiasserini +3 · 25 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Blind Source Separation Techniques #Combinatorics #Computer science #Dimension (graph theory) #Eigenvalues and eigenvectors #Field (mathematics) #Image and Signal Denoising Methods #Independent and identically distributed random variables #Mathematics #Mean squared error #Metric (unit) #Radar #Random variable #Signal processing #Signal reconstruction #Sparse and Compressive Sensing Techniques #Statistics #cs.IT #math.IT
paper · pdf · doi:10.1109/tsp.2008.925953
published in IEEE Transactions on Signal Processing 56(9), 4274-4285 (Institute of Electrical and Electronics Engineers) · To appear on IEEE Transactions on Signal Processing, 2008
arxiv created 2008/04/21 · openalex publication_date 2008/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.