Compression limits for random vectors with linearly parameterized second-order statistics

Daniel Romero, Roberto López-Valcarce, Geert Leus

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived - the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors arises naturally when sampling wide-sense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and nonperiodic fashion are provided by considering two of the most common linear compression schemes, which we classify as dense or sparse. It is seen that the maximum compression ratios depend on the structure of the HT subspace containing the covariance matrix of the uncompressed observations. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure. Universal samplers are also proposed to compress unknown HT subspaces.

Original languageEnglish (US)
Article number7017552
Pages (from-to)1410-1425
Number of pages16
JournalIEEE Transactions on Information Theory
Volume61
Issue number3
DOIs
StatePublished - Mar 1 2015

Keywords

  • Compression Matrix Design
  • Compressive Covariance Sensing
  • Covariance Matching

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