Signal restoration using efficient constrained least squares techniques

D. O. Walsh, Michael W Marcellin, P. A. Delaney

Research output: Contribution to journalArticle


The problem of restoring missing samples from a finite time or space domain vector given a portion of its discrete frequency spectrum (DFT) and known bounds on the missing samples is investigated. A matrix-based solution technique is proposed as a numerically efficient alternative to an iterative solution via alternating projections onto convex sets (POCS). The problem is formulated as a set of linear equations that relate the known time and frequency samples to the missing time domain samples. Finitely convergent gradient-based search algorithms are employed to compute the constrained least squares solution to this set of linear equations. It is shown that if the set of linear equations is exactly or overly determined the POCS iteration will converge to the solution computed by the gradient search method. The numerical efficiency of the proposed technique is demonstrated by a 1-D slab profile inversion example.

Original languageEnglish (US)
Pages (from-to)3176
Number of pages1
JournalIEEE Transactions on Signal Processing
Issue number12
Publication statusPublished - 1996


ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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