Recursive implementation of the distributed Karhunen-Love transform

Alon Amar*, Amir Leshem, Michael Gastpar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


In the distributed linear source coding problem, a set of distributed sensors observe subsets of a data vector with noise, and provide the fusion center linearly encoded data. The goal is to determine the encoding matrix of each sensor such that the fusion center can reconstruct the entire data vector with minimum mean square error. The recently proposed local Karhunen-Love transform approach performs this task by optimally determining the encoding matrix of each sensor assuming the other matrices are fixed. This approach is implemented iteratively until convergence is reached. Herein, we propose a greedy algorithm. In each step, one of the encoding matrices is updated by appending an additional row. The algorithm selects in a greedy fashion a single sensor that provides the largest improvement in minimizing the mean square error. This algorithm terminates after a finite number of steps, that is, when all the encoding matrices reach their predefined encoded data size. We show that the algorithm can be implemented recursively, and compared to the iterative approach, the algorithm reduces the computational load from cubic dependency to quadratic dependency on the data size. This makes it a prime candidate for on-line and real-time implementations of the distributed Karhunen-Love transform. Simulation results suggest that the mean square error performance of the suggested algorithm is equivalent to the iterative approach.

Original languageAmerican English
Article number5504834
Pages (from-to)5320-5330
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - Oct 2010
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received August 23, 2009; accepted June 11, 2010. Date of publication July 08, 2010; date of current version September 15, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Mathini Sellathurai. This work was supported in part by NWO-STW under the VICI program (Project 10382), and by the 3TU.CeDICT: Centre for Dependable ICT Systems.


  • Distributed compression
  • distributed Karhunen-Love transform
  • distributed transforms
  • principal component analysis
  • source coding
  • transform coding


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