Research on Star Image Noise Filtering Based on Diffusion Model of Regularization Influence Function

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1 016 Sith International Conference on Intrumentation & Meaurement Computer Communication and Control Reearch on Star Image Noie Filtering Baed on Diffuion Model of Regularization Influence Function SunJianming School of computer and information engineering Harbin Univerity of Commerce Harbin China Dai Lijun School of management Harbin Univerity of Commerce Harbin China Abtract A the noie filtering of tar map i pecial noie filtering need to remain the detail on the edge of tar in the baic phae of identifying tar. The author propoe a method of tar image noie filtering baed on diffuion model of regularization influence function by uing Tukey diffuion model and improved PM model. Thi method can etract boundary point et by derivative operator do noie filtering according to pace ditribution characteritic of original piel and noie piel and fulfill the goal of retoring the edge by boundary condition given. In the imulation eperiment of ordinary image and tar map thi method i ued to how better capability of noie filtering and remain the edge of feature image effectively. Compared to ordinary diffuion function algorithm thi algorithm i lower by 13.6% in the apect of mean abolute error higher by 6.1% on Peak Signal to Noie Ratio. Thee tatitic can illutrate that thi method i better than ordinary diffuion function method in term of filtering ability which more applie to do noie filtering of tar map.. Keyword Star map noie; regularization; influence function; diffuion function I. INTRODUCTION Celetial navigation i a kind of independent navigation method which can be ued to provide precie attitude and location information for atellite deep pace detector and huttle.star enor i an important device in navigation. Generally tar map we get from tar enor ha noie o removing noie become neceary before we identify the tar map. The removal of noie in image i the baic tep in proceing image. In thi proce the real image that i fit for proceing i got from the obervation map with noie. We can define it a ill-poed invere problem which ha been reearched further in a lot of literature. However mot reearche are to the additive Gauian White Noie. In CCD tar enor baed on photon counting imaging ytem image we got are uually polluted by photon noie which abide by the tatitical rule of Poion Ditribution that i it i not additive noie and it noie force and variance have ignal dependence. The higher piel brightne i the more it intervention ha. Therefore removing Gauian noie i a tough tak. The uual method of removing Gauian noie i to do Variance Stabilization Tranform in pace domain or tranform domain of obervation map. Thi method ha Ancombe Haar-Fiz CVS tranform and o on. After tranform image tatitic i Gauian ditribution imilar to homokedaticity of variance. Thi kind of tar map ha the ame problem a Gauian denoiing of ordinary image. Wiener Filter Wavelet threhold and o on can be ued to proce noie filtering and final denoiing tar map can be got by Variance Stabilization Tranform. With thi method and Multicale geometric tranform we can get better eperiment image. However thi method i alo limited becaue not all image tend to Gauian ditribution after Variance Stabilization Tranform. Thi method i not proper when low light quantum number i not too much. Variance Stabilization Tranform i non-linear tranformation which i bad to analyze and optimize the performance of denoiing algorithm. Star noie filtering done by regularization influence function diffuion model need not be tranformed which can help avoid ome difficultie caued by tatitic repetition. Thi method can remove noie and remain the edge to the maimum etent[8-9]. Thi method et the threhold via derivative operator in order to ditract image boundary point et with noie. After that thi method can eliminate noie according to the irrelevance of noie point ditribution in the image and retore image boundary according to the relevance of other non-noie point. Finally removing noie i done by regularization influence function diffuion algorithm. Filtering algorithm propoed by thi paper can remove noie and remain edge feature in the image which lay a good foundation for identifying tar map. II. BUILDING OF MODEL Regularization influence function diffuion model i a minimization problem of energy function made by moothing term and fidelity term which can be decribed by min EuminE ue D u (1) In thi equation fidelity term can be hown by u the degree of imilarity of image after diffuion can be decribed by E D u u I ddy () ED /16 $ IEEE DOI /IMCCC

2 In equation () I mean image gray which need to be proceed and u mean gray after diffuion and mean image pace. E u E u u i moothing term in which parameter are each order patial derivative of image gray. The firt order derivative i a grad of image gray. The econd derivative i Laplace operator of image intenity. a a fidelity parameter play a role in mooth degree of image after diffuion. The definition of the moothing term of regulation model of the firt order derivative can be hown a E u u ddy (3) Image diffuion equation can be hown a u divg u u (4) t Combining (3) and (4) we can get diffuion influence function which can be hown a u u u gu u (5) t u u In equation (5) gu can be called diffuion u influence function in which u i a critical item. Smoothing degree of image lie in it. Therefore we need to find a better u function uch a u u. It correponding regulation model i Tikhonov and moothing term i E u u ddy. When u u regulation model i TV model and moothing term i E u uddy. Thee two model can be defined a p E u u ddy in which 0 p. Thi model become a TV model in a broad ene. Firt confirm that you have the correct template for your paper ize. Thi template ha been tailored for output on the A4 paper ize. If you are uing US letter-ized paper pleae cloe thi file and download the file MSW_USltr_format..1 Diffuion propertie of regulation model Becaue p play a role in diffuion regulation of image in one-dimenional pace can be analyzed a u g u u follow: t If u gu u then u t u u u Here u u. In equation (6) when u 0 diffuion; when u 0 when 0 (6) 0 there i the forward 0 there i the backward diffuion; there i no diffuion. u. Regularized PMPerona-Malik model PMPerona-Malikmodel i often defined a u divcu u t u0 u0 (7) In equation (7) u i image intenity and u i gradient operator and div i divergence and c i diffuion coefficient.(nonnegative decreaing function with upper and lower bound) But becaue of ill-poedne of PM model patial regularization need to be done. u t divc G ut ut (8) t Thi proce can do Gauian regularization to u and replace u with G ut. Temporal regularization of PM model can be defined a u div c v u t v 1 u v t (9) u0 u 0 v0 G * u 0 In equation (10) when 0 mean delay v i regulation of delayed time to u. To harpen edge the value of diffuion coefficient on the edge i negative. Thi model can be pecified a u divcu u t uy0 u0 y (10) And n 1 0 k k f f m k c a b 1 kb w kb w w 0 other (11).3 Tukey Model Tukey diffuion function i the one with better performance whoe form i 136

3 1 u 1 cu T u T 0 ele (1) When image i le than T u of different direction in image depend on diffuion coefficient. When image i more than T diffuion proce will be topped. Once the value of T i et piel point where noie gradient i more than T in image can be kept. That i to ay if a majority of noie point gradient are more than T reult of removing noie are not ideal. To thi ituation thi paper employ many regularization influence function to remove noie in image. Becaue there are difference between function noie can be eparated epecially when difference become larger. III. FULFILLMENT OF MODEL ALGORITHM 3.1 Image denoiing removal model If noie in an image i independent it degradation model can be hown a g y f yn y (13) In equation (13) f y n y and g y repreent original image noie and image with noie. Condition which are ued to identify noie are: 1) no other high gradient point in the pro domain around g y ; )that there are difference between high gradient point in the pro domain and g y. All the above can be identified a noie point which are removed by moothing filtering. 3. Boundary Retoring Model Boundary meage in original image f y cannot be conveyed by image with noie g y o a boundary retoring model i needed to redefine boundary in order to retore the edge. The definition of thi model i that if boundary point g y doen t contain no other boundary algorithm in pro domain there i weak relevance and boundary will not be kept; if there i a boundary point in pro domain and thi point i imilar to it thi point ha trong relevance with g y and they have imilar boundary which can be conidered that it boundary lot when removing noie i done. Retoring it boundary i like Figure 1 Fig.1 The tar boundary identification and rehabilitation 3.3 Filtering proce Step one Initializing parameter: Identify image I y and I y t I y before diffuion i done. t 0 Step two: take a moving window of pro domain then get diffuion direction. It direction derivative i I y t the pecific algorithm i that it dicretization can be conveyed by Iihjhnt in which t h are repectively time interval and pace interval.in thi way we can get direction derivative. Step Three Ue to calculate diffuion coefficient g d. Step Four According to dicrete boundary retoring 1 formula I y Iy g t 1 d I y d 1 t calculate the image of removing noie. Step Five Check topping condition and retart thi proce from Step Two if topping condition are not conformed to. IV. EXPERIMENT RESULTS AND ANALYSIS We can tet L1/ regulation algorithm i effective by imulation eperiment of many image and removing noie algorithm baed on image of diffuion function.thi method ue local gradient of real part of the image to control diffuion intenity parameter in order to fulfill different diffuion velocity in different gradient region.the more the iteration tep are the more iteration are. And finally the aim to remove noie in the image can be achieved. Thi method can be called diffuion function method. The image which are ued in the imulation eperiment are teting image 137

4 (51*51matlab) and tar map (51*51) whoe tellar magnitude i brighter than 7.0. Thi paper compare quality of removing noie by thee two algorithm from the apect of viual effect and parameter. Parameter include MAE and PSNR. Thee two parameter can be defined a follow: u i j uij MAE i j MN (14) 10log10 ma u PSNR u i j uij i j MN (15) In equation (14) and (15) u i image without noie u i the image after removing noie. N and M correpond to length and width. i j are piel poition indication. Adaptability of MAE for tatitic characteritic i bet to Poion denity function. In the eperiment (a) in Figure () and (3) are origin image; (b) are Gauian additional noiy image; (c) are image denoiing by diffuion function algorithm of uing diffuion function algorithm; (d) are image denoiing by regularization influence function diffuion method. There are ditinct advantage in the image by uing regularization method. (a) origin image (b) Noiy image (c) Diffuion function algorithm (d) The algorithm of image of image denoiing denoiing Fig.3 Star Gau noie image to compare de-noiing algorithm and eperimental reult In the eperiment of removing noie in tar map we can comparing convergence function oberve boundary convergence rate by diffuion method and regularization influence function diffuion method. Jut like Figure (3) when gradient value i influence function between regularization influence function diffuion method and PM function model and Tukey function model i increaing greatly a image intenity become tronger. In thi way noie can be filtered better. (a) origin image (b) Noiy image (c) Diffuion function algorithm (d) The algorithm of image of image denoiing denoiing Fig. Gau noie Lena image to compare de-noiing algorithm and eperimental reult Fig.4 Comparion of the convergence peed of image intenity Comparion of quantitative indicator denoiing performance in two algorithm i hown in the following table. 138

5 Tab.1 Comparion of quantitative indicator denoiing performance table Image Figure 1 a Figure a Perfor mance indicat or Degra ded image Ordinary diffuion algorithm Regularizatio n influence function diffuion algorithm MAE PSNR( db) MAE PSNR( db) 3 From Table 1 ditinct advantage can be hown in denoiing by uing regularization influence function diffuion algorithm. [6] SUN J M. Chattering-Free Sliding-Mode Variable Structure Control of Delta Operator Sytem Journal of Computational and Theoretical Nanocience 014 pp [7] WANG L Y WEI Z H LI X X. Morphological component analyi for tomography recontruction Journal of Image and Graphic 01 pp.0-6. [8] LI W H DONG Y L TANG S. Regularized blind image retoration baed on multi-norm hybrid contraint Optic and Preciion Engineering [9] ZHOU L Y ZHANG B YANG Y. Image blind deblurring baed on uper total variation regularization with elf-adaptive threhold Optic and Preciion Engineering 01 pp [10] LIANG D LIANG Z BAO W Z et al.. Image denoiing algorithm baed on non-local regularized pare repreentation Sytem Engineering and Electronic 013 pp [11] XIU J GENG R T J HONG G..et al.. Diffeomorphic Image Regitration of Diffuion MRI Uing Spherical Harmonic IEEE Tran.Medical Imaging. 011 pp [1] Taeg Sang Cho Zitnick C L Johi N et al.. Image Retoration by Matching Gradient Ditribution IEEE Tranaction on Pattern Analyi and Machine Intelligence 01 pp V. CONCLUSION In the frame of regularization boundary influence function thi paper employ PM model and Tukey model a diffuion function to build tar map denoiing filtering method baed on regularization influence function diffuion model by uing regular term under diffuion function. Thi method avoid VS tranform and handle Gauian noie directly. By imulation tet on ordinary image and tar map with Gauian additional noie and comparing with ordinary diffuion function algorithm we can know from the eperiment reult that indicator of MAE in regularization influence function diffuion algorithm decreae by 13.6% and indicator of PSNR increae by 6.1%. Hence we can identify the poition of tar in the denoiing image which lay a good image data foundation for the following identification of tar map. ACKNOWLEDGE Thi work wa upported by Heilongjiang province natural foundation project(grant No. F0144). REFERENCES [1] Lefkimmiati S Uner M. Poion Image Recontruction with Heian Schatten-Norm RegularizationIEEE Tranaction on Image Proceing 013 pp [] HU Y YANG J ZHOU Y. Multicale Wiener Filter for the Etimation of Signal Embedded in1/f Noie Acta Electronica Sinica 003 pp [3] LI Y F LI M J SI G L et al.. Noie analyzing and proceing of TDI- CCD image enor Optic and Preciion Engineering 007 pp [4] DENG W J ZHENG L G SHI Y L et al.. Dwell time algorithm baed on matri algebra and regularization method Optic and Preciion Engineering 007 pp [5] GUO Y C WANG A N GAO C. Blind image retoration algorithm baed on pace-adaptive and regularization Optic and Preciion Engineering 008 pp