Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications
Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Damped Newton Algorithms for Matrix Factorization with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Analysis and design of minimax-optimal interpolators
IEEE Transactions on Signal Processing
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A non-iterative methodology for the interpolation and regularization of multidimensional sampled signals with missing data resorting to Principal Component Analysis (PCA) is introduced. Based on unbiased sub-optimal estimators for the mean and covariance of signals corrupted by zero-mean noise, the PCA is performed and the signals are interpolated and regularized. The optimal solution is obtained from a weighted least mean square minimization problem, and upper and lower bounds are provided for the mean square interpolation error. This solution is a refinement to a previously introduced method proposed by the author Oliveira (Proceedings of the IEEE international conference on acoustics, speech, and signal processing--ICASSP06, Toulouse, France, 2006), where three extensions are exploited: (i) mean substitution for covariance estimation, (ii) Tikhonov regularization method and, (iii) dynamic principal components selection. Performance assessment benchmarks relative to averaging, Papoulis-Gerchberg, and Power Factorization methods are included, given the results obtained from a series of Monte Carlo experiments with 1-D audio and 2-D image signals. Tight upper and lower bounds were observed, and improved performance was attained for the refined method. The generalization to multidimensional signals is immediate.