Reduced-Dimension Linear Transform Coding of Distributed Correlated Signals With Incomplete Observations

• Published in: IEEE transactions on information theory Vol. 55; no. 6; pp. 2848 - 2858
• Main Authors: Nurdin, H.I., Mazumdar, R.R., Bagchi, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Coders; Codes; Coding; Coding, codes; Correlation; Cryptography; Data encryption; Distributed computing; Distributed signal processing; Exact sciences and technology; Gaussian; Information theory; Information, signal and communications theory; innovations; Karhunen-Loeve transforms; Karhunen-LoÈve transform; Mathematics; Miscellaneous; Normal distribution; optimal linear estimation; Optimization; Random variables; Relays; Representations; Sensor phenomena and characterization; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal representations; Signal, noise; Technological innovation; Telecommunications and information theory; Transform coding; Transforms; Second order; Karhunen Loeve transformation; Karhunen―Loève transform; Optimal estimation; Signal representation; Mean estimation; Distributed processing; innovations; Linear coding; Innovation; Covariance; optimal linear estimation; Distributed signal processing; Transform coding; Linear transformation; Signal processing; Linear estimation; Random variable
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2018349

We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding the optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular, this leads to the study of finding the optimal Karhunen-Loeve basis based on the censored observations. The problem has been considered previously by Gastpar, Dragotti, and Vetterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problem.