Signal processing in dual domain by adaptive projected subgradient method

Masahiro Yukawa, Konstantinos Slavakis, Isao Yamada.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The goal of this paper is to establish a novel signal processing paradigm that enables us to find a point meeting time-variable specifications in dual domain (e.g., time and frequency domains) simultaneously. For this purpose, we define a new problem which we call adaptive split feasibility problem (ASFP). In the ASFP formulation, we have (i) a priori knowledge based convex constraints in the Euclidean spaces RN and RM and (ii) data-dependent convex sets in RN and RM; the latter are obtained in a sequential fashion. Roughly speaking, the problem is to find a common point of all the sets defined on RN such that its image under a given linear transformation is a common point of all the sets defined on RM, if such a point exists. We prove that the adaptive projected subgradient method (APSM) deals with the ASFP by employing (i) a projected gradient operator with respect to (w.r.t.) a 'fixed' proximity function reflecting the convex constraints and (ii) a subgradient projection w.r.t. 'time-varying' objective functions reflecting the data-dependent sets. The resulting algorithm requires no unwanted operations such as matrix inversion, therefore it is suitable for realtime implementation. A convergence analysis is presented and verified by numerical examples.

Original languageEnglish (US)
Title of host publicationDSP 2009:16th International Conference on Digital Signal Processing, Proceedings
DOIs
StatePublished - Nov 20 2009
EventDSP 2009:16th International Conference on Digital Signal Processing - Santorini, Greece
Duration: Jul 5 2009Jul 7 2009

Publication series

NameDSP 2009: 16th International Conference on Digital Signal Processing, Proceedings

Other

OtherDSP 2009:16th International Conference on Digital Signal Processing
Country/TerritoryGreece
CitySantorini
Period7/5/097/7/09

Keywords

  • Adaptive projected subgradient method
  • Convex feasibility problem
  • Projected gradient
  • Split feasibility problem

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