A Signal Processing Approach to Generalized 1-D Total Variation

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. Her...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-11, Vol.59 (11), p.5265-5274
Main Authors: Karahanoglu, F. I., Bayram, I., Van De Ville, D.
Format: Article
Language:English
Subjects:
Applied sciences
Derivatives
Detection, estimation, filtering, equalization, prediction
Dictionaries
Differential operators
Driving
Exact sciences and technology
Flexibility
Image edge detection
Image processing
Information, signal and communications theory
Linear systems
Noise reduction
Operators
Regularization
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
sparsity
Telecommunications and information theory
Television
total variation
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2164399