A Signal Processing Approach to Generalized 1-D Total Variation

Karahanoglu F. I., Bayram I., Van De Ville D.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.59, no.11, pp.5265-5274, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 11
  • Publication Date: 2011
  • Doi Number: 10.1109/tsp.2011.2164399
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5265-5274
  • Istanbul Technical University Affiliated: No


Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rather limited model for many applications. Here we generalize conventional TV in 1-D by extending the derivative operator, which is within the regularization term, to any linear differential operator. This provides flexibility for tailoring the approach to the presence of nontrivial linear systems and for different types of driving signals such as spike-like, piecewise-constant, and so on. Conventional TV remains a special case of this general framework. We illustrate the feasibility of the method by considering a nontrivial linear system and different types of driving signals.