Study Of Turbulence-degraded Image Restoration Technology Based On Fractional Fourier Transform

When an optical beam propagates through the air flow around an aircraft, the optical wave front would be distorted due to the air density fluctuation, which would largely debase the performance of the airborne optical systems. These effects cause received images to attenuate, out of focus and dithering, make object identification very difficult. Owing to the fact that the point spread function of turbulence is unknown, changeable with time, and hard to be described by mathematics models, a lot of problems have been existed in restoration algorithms. A new time-frequency analytic tool--fractional Fourier transform has been studied for turbulence-degraded images, and the main contributions of this paper are given below.1. The effects on imaging systems came from turbulence flow have been studied, development of aero-optics effects correction technology has been summarized, and restoration algorithms for turbulence-degraded images have been studied.2. Study of numerical simulation for aero-optical effects helps to comprehend turbulence-degraded images caused by turbulence. A platform with flat window has been computed with the proposed method. Favre averaging Navier-Stokes equations have been solved with LU-SGS iteration, Van-Leer flux vector difference or splitting schemes and MUSCL windward off-set forms. Two-equation k-ωSST model and J-B model have been chosen as turbulence models. Light wave transmission effects have been computed by geometrical optics tracking means and transmit-focus system.3. Principles and characters of the fractional Fourier transform have been expatiated, and decompounded discrete numerical calculation algorithms have been studied, making it possible to compute FrFT simple as DFT. Information of energy, amplitude and phase of images in fractional Fourier domain have been analyzed, and the double domain character has been verified.4. Filtering in fractional Fourier domains has been studied. Optimal filtering can be achieved by choosing appropriate angle of swing to fit the object to avoid the coupling. This method is much better than that in classic Fourier domain. Time-varying degraded images with nonstationary processes noises have been experimented, and smaller MSE of restoration images have been achieved than that of using classic Fourier filtering.5. Phase recovery algorithm with the fractional Fourier transform has been developed. Phase recovery algorithm has been translated into de-autocorrelation, and iterations are carried through during each other to solve the problem of stagnation on local optimal solution and to improve convergence probability. Least-square conjugate gradient has been adopted to solve de-autocorrelation equations to improve the speed of convergence. Fractional order has been studied, optimal extremism have been proved, and experimental results show that the proposed algorithm is more effective than traditional method for both blur and turbulence-degraded images.