Abstract
This paper presents a signal and image recovery scheme by the method of alternating projections onto convex sets in optimum fractional Fourier domains. It is shown that the fractional Fourier domain order with minimum bandwidth is the optimum fractional Fourier domain for the method employing alternating projections in signal recovery problems. Following the estimation of optimum fractional Fourier transform orders, incomplete signal is projected onto different convex sets consecutively to restore the missing part. Using a priori information in optimum fractional Fourier domains, superior results are obtained compared to the conventional Fourier domain restoration. The algorithm is tested on 1-D linear frequency modulated signals, real biological data and 2-D signals presenting chirp-type characteristics. Better results are obtained in the matched fractional Fourier domain, compared to not only the conventional Fourier domain restoration, but also other fractional Fourier domains.
| Original language | English |
|---|---|
| Pages (from-to) | 675-689 |
| Number of pages | 15 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 2010 |
| Externally published | Yes |
Funding
The authors are supported by the Scientific and Technological Research Council of Turkey, TUBITAK under the grant of Project No. 105E078. The authors thank Curtis Condon, Ken White, and Al Feng of the Beckman Institute of the University of Illinois for the bat data and for permission to use it in this paper.
| Funders | Funder number |
|---|---|
| TUBITAK | 105E078 |
| Türkiye Bilimsel ve Teknolojik Araştirma Kurumu |
Keywords
- Fractional Fourier transform
- Fractional Fourier transform order estimation
- Image recovery
- Method of alternating projections
- Signal recovery