Motion-blurred star image acquisition and restoration method based on the separable kernel Honglin Yuana, Fan Lib and Tao Yuc

Transcription

1 5h Inernaional Conference on Advanced Maerials and Compuer Science (ICAMCS 206) Moion-blurred sar image acquisiion and resoraion mehod based on he separable kernel Honglin Yuana, Fan Lib and Tao Yuc Beihang Universiy, Beijing 009, China. a yuanhonglin@buaa.edu.cn, blifan@buaa.edu.cn, cyrock@buaa.edu.cn Keywords: sar racker, non-uniform moion blur, simulaion, resoraion. Absrac. The sar racker is supposed o have he highes accuracy among differen ypes of aiude measuremen devices. However, images aken by he sar racker under dynamic condiions are ofen blurred, especially in deep space exploraion, which limis is high dynamic performance and accuracy. This paper addresses how o simulae blurred sar images and remove image blurs ha arise when he sar racker is under dynamic condiions of angular vibraions and roaions. We classify and model sar racker s roaion and angular vibraion. Afer ha, we simulae he blurred sar images caused by composie moion of roaions and angular vibraions. Afer acquiring he moion-blurred sar image, a resoraion mehod is proposed o resore i. The simulaion resuls indicae ha our approach makes i possible o model and remove a wider class of blurs han previous approaches, including uniform blur as a special case and he exracion accuracy of sar spo cenroid is improved significanly using he resored sar image compared wih he blurred one. Inroducion Aiude deerminaion plays an imporan role on he opical auonomous navigaion, paricularly in urgen demand for deep-space mission. The sar racker is supposed o have he highes accuracy under sable condiions among differen ypes of aiude measuremen devices []. Tradiion approaches for sar cenroid exracion require enough energy and good shape of sars. However, in deep-space exploraion, he apparen magniude of navigaion sars used for opical auonomous navigaion is high, he exposure ime and focal lengh are long, hese limiing sar rackers updae rae and dynamic performance [2], which is more likely o lead o blurred sar images. However, i is no helpful o use radiional mechanical, opical approaches [3, 4] which are based on hardware o resore he moion-blurred sar image. For hese reasons, sudying he moion-blurred sar image acquisiion and resoraion mehods have imporan heoreical meaning and engineering applicaion value for he sar racker and is helpful o improve he sar racker dynamic performance. While significan progress has been made recenly owards simulaing moion-blurred sar images, mos of curren approaches model he blurred sar image as he convoluion of a sharp image wih a spaially uniform kernel. Zhang [5] simulaed spaially varying moion-blurred sar images, bu only he roaion was considered. Sun [6] proposed a smearing moion model of he sar spo and only simulaed blurred sar images wih uniform blur kernel. Wang [7] buil moion-blurred models and hen simulaed muliple blurred sar images which conained boh uniform and non-uniform blur kernels. However, his mehod canno exacly describe he sar racker s moion pah. If he blur kernel for each pixel has he same form, he problem of resoraion is generally referred o as no-blind deconvoluion, for which sandard echniques such as he Wiener filer[8] or he Richardson-Lucy[9] exiss. However, hese resoraion algorihms have generally been limied o he case of uniform blur. To resore images wih spaial-varian blurs, Wang [7] used he sep-by-sep mehod o deblur he moion-blurred sar images, bu his mehod is no useful when he blurred images conain non-uniform blurs The auhors - Published by Alanis Press 367

2 All in all, recen work mosly focuses on simulaion and resoraion of blurred sar images conaining uniform blur caused by single angular moion or vibraion. However, lile research has been done on blurred sar image caused by he combine of roaion and angular vibraion. Simulaion mehod of he blurred sar image In his secion, we use an inegraion of he clear sar image under a sequence of planar projecive ransforms o ge he blurred sar image. Supposing ha an image f( xy, ) undergoes planar moion and x o () and y o () are he ime-varying componens of moion in he X and Y direcions respecively, he oal exposure a any poin of he CCD is obained by inegraing he insananeous exposure over he ime inerval during which he image sysem shuer is open. T is he exposure ime and he blurred sar image gxy (, ) can be obained by[0] g( x, y) = T f [ x x 0 0( ), y y0( )] d () Subdividing exposure imet ino M equal porions, i follows ha T g( x, y) = f [ x - x ( ), y - y ( )] d M - = f[ x- x0( i), y-y0( i)] M i= 0 (2) where M T and f[ x x0( i), y y0( i)] is he projecive ransformaion of a clear sar image. Depending on he moion parameers obained by he navigaion sysem, we can ge he rajecory funcion of he blur kernel on image plane and hen he blurred sar image wih roaions and angular vibraions can be obained. Blurred sar image resoraion In his secion, we describe how o use he Richardson-Lucy algorihm o resore he blurred sar image. Richardson-Lucy algorihm, a nonlinear raio-based mehod, is effecive for processing Poisson noise in a sar image and can avoid ringing arifacs ha usually exis in linear resoraion mehods. I has he advanages of aking only a few minues, even on large sar images and always produces nonnegaive gray-level values, which gives resuls ha make beer physical sense. This mehod maximizes a Poisson-saisics sar image model likelihood funcion, given by[9] + Bx ( ) O ( x) = O ( x) K( x) K( x) O ( x) (3) where Bxis ( ) he measured blurred sar image, O ( x) is he k-h esimaion of he sharp image, O 0 ( x ) = Bx ( ), K ( x ) is he blur kernel, K ( x ) is he ranspose of ha flips he shape of upside-down and lef-o-righ, is he convoluion operaion. Given he esimaed blur kernel, he sharp sar image can be obained by Eq.(3). However, for a non-uniform blurred sar image, he Richardson-Lucy algorihm is no suiable. In his case, we use he projecive moion Richardson-Lucy algorihm [] o resore he blurred sar image. The general form of his algorihm is + ( ) = ( ) M O x O x Ei ( x) M i= (4) Bx ( ) where Ei ( x) = is he residual error beween he real blurred image B and he M O ( ) M i i x = M prediced blurred image B = O ( x). M is he number of accumulaion. In deep-space i= M i 368

3 exploraion, SINS navigaion sysem is inroduced o improve he precision and sabiliy of navigaion sysem, so ha cerain moion informaion can be derived from SINS, including vehicle speed, angular rae ec. The rajecory can be obained based on he informaion. Consequenly, he resoraion algorihm can be used o resore he blurred sar image. Simulaion and analysis Based on he simulaion mehod, he blurred sar image wih roaion and angular vibraion is shown in Fig. Fig. The blurred sar image wih roaion and angular vibraion. where he displacemen caused by roaion around XC axis is 0 pixels, he roaional angular o velociy is wz = 0 / s around Z C axis, he vibraion ampliude is A = 3pixels, and is frequency is f = 00Hz wih an angle of 30 o o he horizonal, he exposure ime is 400ms. Fig.2 shows he resuls of blurred sar image and able shows he comparison of exracion errors before and afer he resoraion. (a) (b) (c) Fig.2 The comparison of shape and gray disribuion of one sar before and afer resoraion.(a) is he original sar, (b)is he blurred sar, (c) is he resored sar. 369

4 Index of sar spo Table The comparison of he sar cenroid agains blurred sar image Coordinae Coordinae of Exracion Coordinae of of original blurred sar error resored sar sar image image (pixel) image (pixel) (pixel) (pixel) Exracion error (pixel) (8,55) (70.5,59.37) (-0.49,4.37) (80.7,55.20) (-0.29,0.20) 2 (5,69) (05.34,76.93) (-9.66,7.93) (5.07,69.3) (0.07,0.3) 3 (6,76) (4.08,80.48) (-.92,4.48) (7.68,75.2) (.68,-0.88) 4 (24,43) (8.25,50.25) (-5.75,7.25) (24.07,42.95) (0.07,-0.05) 5 (232,59) (226.72,60.55) (-5.28,.55) (232.03,59.7) (0.03,0.7) 6 (23,89) (227.43,90.57) (-3.58,.57) (23.02,89.02) (0.02,0.02) 7 (56,23) (54.06,223.85) (-.94,0.85) (56.,23.45) (0.,0.45). The local enropy mehod [2] is used o exrac he cenroid of sar spos. I appears ha he effecs of roaion and angular vibraion have grea impac on he exracion accuracy of sar spo and he exracion errors of x or y can be larger han en pixels for sar cenroid wihou he resoraion. Afer he resoraion, he exracion errors of x or y are wihin subpixel range, which indicaes ha he effecs caused by roaion and angular vibraion can be ignored by he resoraion. Conclusions The moion-blurred sar image acquisiion and resoraion mehod are sudied when he sar racker has long focal lengh and exposure ime and small visual angle in his paper. Bade on simulaion mehod, blurred sar images are obained and a resoraion mehod is inroduce o resore he blurred sar image. Afer he resoraion, he exracion error is wihin he subpixel level, indicaing ha he proposed mehod is boh effecive and feasible. The work in his paper provides he heory basis for improving he sar racker dynamic performance and he celesial opical auonomous navigaion accuracy. References [] Liebe C C. Accuracy Performance of Sar Trackers-A Tuorial, J. IEEE Transacions on Aerospace & Elecronic Sysems. 38 (2002) [2] Jia H, Yang J K, Li X J, e al. Sysemaic error analysis and compensaion for high accuracy sar cenroid esimaion of sar racker, J. Science China Technological Sciences. 53 (200) [3] Gong D, Yanpeng W U, Xin L U. An Aemp a Improving Dynamic Performance of Sar Tracker by Moion Compensaion, J. Aerospace Conrol & Applicaion, [4] Fei X, Nan C, Zheng Y, e al. A Novel Approach Based on MEMS-Gyro's Daa Deep Coupling for Deermining he Cenroid of Sar Spo, J. Mahemaical Problems in Engineering, 202. [5] Weina Z, Wei Q, Lei G. Blurred Sar Image Processing for Sar Sensors under Dynamic Condiions, J. Sensors. 2 (202) [6] Ting S, Fei X, Zheng Y, e al. Smearing model and resoraion of sar image under condiions of variable angular velociy and long exposure ime, J. Opics Express. 22 (204) [7] Wu X, Wang X. Muliple blur of sar image and he resoraion under dynamic condiions, J. Aca Asronauica. 68 (20) [8] Wei Q, Weina Z. Resoraion of Moion-blurred Sar Image Based on Wiener Filer, C. Proceedings of he 20 Fourh Inernaional Conference on Inelligen Compuaion Technology and Auomaion - Volume 02. IEEE Compuer Sociey

5 [9] Chu Y L, Shao-Chun L I, Wang M. An Algorihm of Modified Richardson-Lucy Regularizaion Approach for Image Resoraion, J. Journal of Langfang Teachers College, 202. [0] Wang Xiaoyan, Yan Jiqing, Tang Yi, e al. Simulaion and analysis of high frequency vibraion fuzzy image, J. opical echnology. 37 (20) [] Tai Y W, Tan P, Brown M S. Richardson-Lucy Deblurring for Scenes Under Projecive Moion Pah, J. IEEE Transacions on Paern Analysis & Machine Inelligence. 33 (200) [2] Tian Yulong, Wang Guangjun, Fang Jiancheng, e al. Sar sar sar map exracion mehod based on local enropy, J. Journal of Harbin Insiue of Technology. 37 (2005)