| Study of image restoration is of practical significance and essential applied value. Previous researches on degraded image restoration are all based on the images acquired from circular-aperture optical systems. Among the three common models for image degradation point spread function (PSF), motion blur, unfocused and Gaussian model, the last two supposes using circular aperture. For most of other researches on image restoration beyond these three models, to satisfy the characteristics of circle symmetry is required.With the development of science and technology, optical systems having iris diaphragms, which are regular polygon apertures generally, are increasingly broadly applied in most fields. For the aim to increase the accuracy and efficiency of image restoration, it is necessary to study the corresponding deconvolution methods in the research of image restoration according to the imaging mechanism of degraded images. In the existing literatures, there are few researches on restoration of degraded images from iris diaphragms. In this dissertation, researches on degraded image restoration from iris diaphragms are focused.The mathematical model of degraded images g ( x, y ) = h( x, y )* f ( x, y ) + n( x, y) In which, g , f , h and n are observed image, original image, PSF and noise respectively.Image restoration means to compute the original image f ( x, y ) while given the observed image g ( x, y ).According to the characteristics of Fourier transformation, the above model in frequency domain is G( u , v) = H (u , v) F (u , v) + N (u , v)In which G , H , Fand N are the Fourier transformation of g , h , f , and n respectively.The contributions of this dissertation are as follows.(1) Present the PSF model of regular polygon. (?)This PSF model depicts the out-of-focus degradation of regular-polygon aperture in nature, and is important to accurately compute the out-of-focus PSF of regular-polygon aperture.(2) Present and prove the zero-point distribution theorem of Fourier transformation (?) of out-of-focus regular hexagon PSF in theory,Theorem 5.1 Given anyα∈[0,1] , H2(t ,α)hasonly one zero point while t∈(?)Theorem 5.2 Given anyα∈[0,1], H2(t,α) has only one zero point while t∈[π,(?)π].In which, H2(t ,α) is the transform of H0(u , v ).These two theorems prove that there exist zero points for regular hexagon aperture defocused PSF in some intervals of frequency domain and guide the searching of zero points. Define zero point set L1 contain all the points of the first zero point ring. And likely, L2 contain all the points of the second zero point ring (It's not like a'ring', but some kind of twisted regular hexagon). By the guide of the two theorems, we can use numerical methods to get L1 and L2.(3) With all the work above, we propose a fast regular hexagon aperture defocused image restoration method.1) Perform Fourier Transform onto observed image g(x, y) , the output isG(u,v)=(?)(g). 2) Using discrete numercal method get the ?0 and a0 which satisfied (?)3) With a0,ψ0, we an get H(u,v) = H0((u,v)a0Rψ0) the definition of H0(u,v) is in equation (5.4.3).4) Using Wiener Filtering to get F(u,v), the Fourlier Transform of f (x, y).5) Perform the Inversce Fourlier Transform onto F(u,v), we get the restoration image .f(x,y)=F-1(F(u,v))The results of experiments on high PSNR classic images show the method works well.(4) After analyze any regular polygon, we extended the method to regular polygon with even sides.(5) Using the fast regular hexagon aperture defocused image restoration method on unfocused iris image captured by an optical system with regular hexagon aperture, the result is good. To restore unfocused image captured by aoptical system with regular hexagon aperture, our method is better than other methods. It's because other methods surppose the aperture is round shape. The PSF model does not fit the real PSF, so the restore result will be interfered.(6) We designed a"Facial biological feature capture and recgonate system". It can capture two eye's iris, facial feature, and texture of lips in the same time. And it can restore unfocused image part (iris or lip image) in real time.At the end, we give the prospect of the future work in this field.
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