Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/37548
Title: Simultaneous Data Recovery in Image and Transform Domains
Authors: ZHOU JUNQI
Keywords: Image restoration, uncertainty principle, analysis-based approach, split Bregman method
Issue Date: 8-Jan-2013
Source: ZHOU JUNQI (2013-01-08). Simultaneous Data Recovery in Image and Transform Domains. ScholarBank@NUS Repository.
Abstract: This thesis addresses the problem of image recovery from partially given data in both the image and tight frame transform domains. Firstly, we consider a special case for the problem. In that case, the given data are the original image restricted on the support index set in the image domain and the canonical coefficients restricted on the support index set in the transform domain. Motivated by an uncertainty principle, a sufficient condition that ensures the exact recovery of an image is derived. The corresponding recovery algorithm is also given. Furthermore, we compare our algorithm with an existing reconstruction algorithm and see the similarity between them. Then an analysis based model is proposed to handle situations in which exact recovery is impossible or unnecessary, 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.
URI: http://scholarbank.nus.edu.sg/handle/10635/37548
Appears in Collections:Master's Theses (Open)

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