Methods and Applications of Analysis

Volume 20 (2013)

Number 4

Special issue dedicated to the 70th birthday of Stanley Osher: Part I

Guest Editor: Chi-Wang Shu, Brown University

Simultaneous data recovery in image and transform domains

Pages: 425 – 438



Say Song Goh (Department of Mathematics, National University of Singapore)

Zuowei Shen (Department of Mathematics, National University of Singapore)

Junqi Zhou (Department of Mathematics, National University of Singapore)


This paper addresses the problem of image recovery from partially given data in both the image and tight frame transform domains. Motivated by an uncertainty principle, a sufficient condition that ensures the exact recovery of an image is derived. Then an analysis-based model is proposed to handle situations in which exact recovery is impossible, such as when insufficient or only inaccurate data is available. An efficient iterative algorithm is obtained for the model by applying the split Bregman method. Several numerical examples are presented to demonstrate the potential of the algorithm.


image restoration, uncertainty principle, analysis-based approach, split Bregman method

2010 Mathematics Subject Classification

42C40, 49N45

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