Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 20, Issue 10, Pages 2865-2875Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2011.2138148
Keywords
Inconsistent system of equations; large scale; L-0-norm; outlier detection (OD); phase unwrapping (PU)
Funding
- National Nature Science Foundation of China [60802074]
- Program for New Century Excellent Talents in University
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2-D phase unwrapping is an important technique in many applications. However, with the growth of image scale, how to tile and splice the image effectively has become a new challenge. In this paper, the phase unwrapping problem is abstracted as solving a large-scale system of inconsistent linear equations. With the difficulties of large-scale phase unwrapping analyzed, L-0-norm criterion is found to have potentials in efficient image tiling and splicing. Making use of the clustering characteristic of residue distribution, a tiling strategy is proposed for L-0-norm criterion. Unfortunately, L-0-norm is an NP-hard problem, which is very difficult to find an exact solution in a polynomial time. In order to effectively solve this problem, equations corresponding to branch cuts of L-0-norm in the inconsistent equation system mentioned earlier are considered as outliers, and then an outlier-detection-based phase unwrapping method is proposed. Through this method, a highly accurate approximate solution to this NP-hard problem is achieved. A set of experimental results shows that the proposed approach can avoid the inconsistency between local and global phase unwrapping solutions caused by image tiling.
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