Abstract
The windowed Fourier filtering (WFF), defined as a thresholding operation in the windowed Fourier transform (WFT) domain, is a successful method for denoising a phase map and analyzing a fringe pattern. However, it has some shortcomings, such as extremely high redundancy, which results in high computational cost, and difficulty in selecting an appropriate window size. In this paper, an extension of WFF for denoising a wrapped-phase map is proposed. It is formulated as a convex optimization problem using Gabor frames instead of WFT. Two Gabor frames with differently sized windows are used simultaneously so that the above-mentioned issues are resolved. In addition, a differential operator is combined with a Gabor frame in order to preserve discontinuity of the underlying phase map better. Some numerical experiments demonstrate that the proposed method is able to reconstruct a wrapped-phase map, even for a severely contaminated situation.
| Original language | English |
|---|---|
| Pages (from-to) | 4632-4641 |
| Number of pages | 10 |
| Journal | Applied Optics |
| Volume | 55 |
| Issue number | 17 |
| DOIs | |
| Publication status | Published - 2016 Jun 10 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising. / Yatabe, Kohei; Oikawa, Yasuhiro.
In: Applied Optics, Vol. 55, No. 17, 10.06.2016, p. 4632-4641.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising
AU - Yatabe, Kohei
AU - Oikawa, Yasuhiro
PY - 2016/6/10
Y1 - 2016/6/10
N2 - The windowed Fourier filtering (WFF), defined as a thresholding operation in the windowed Fourier transform (WFT) domain, is a successful method for denoising a phase map and analyzing a fringe pattern. However, it has some shortcomings, such as extremely high redundancy, which results in high computational cost, and difficulty in selecting an appropriate window size. In this paper, an extension of WFF for denoising a wrapped-phase map is proposed. It is formulated as a convex optimization problem using Gabor frames instead of WFT. Two Gabor frames with differently sized windows are used simultaneously so that the above-mentioned issues are resolved. In addition, a differential operator is combined with a Gabor frame in order to preserve discontinuity of the underlying phase map better. Some numerical experiments demonstrate that the proposed method is able to reconstruct a wrapped-phase map, even for a severely contaminated situation.
AB - The windowed Fourier filtering (WFF), defined as a thresholding operation in the windowed Fourier transform (WFT) domain, is a successful method for denoising a phase map and analyzing a fringe pattern. However, it has some shortcomings, such as extremely high redundancy, which results in high computational cost, and difficulty in selecting an appropriate window size. In this paper, an extension of WFF for denoising a wrapped-phase map is proposed. It is formulated as a convex optimization problem using Gabor frames instead of WFT. Two Gabor frames with differently sized windows are used simultaneously so that the above-mentioned issues are resolved. In addition, a differential operator is combined with a Gabor frame in order to preserve discontinuity of the underlying phase map better. Some numerical experiments demonstrate that the proposed method is able to reconstruct a wrapped-phase map, even for a severely contaminated situation.
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UR - http://www.scopus.com/inward/citedby.url?scp=84973890932&partnerID=8YFLogxK
U2 - 10.1364/AO.55.004632
DO - 10.1364/AO.55.004632
M3 - Article
AN - SCOPUS:84973890932
VL - 55
SP - 4632
EP - 4641
JO - Applied Optics
JF - Applied Optics
SN - 1559-128X
IS - 17
ER -