Infrared Physics and Technology 93 (2018) 277–285 Contents lists available at ScienceDirect Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared Regular article Error tolerance and eﬀects analysis of satellite vibration characteristics and measurement error on TDICCD image restoration T ⁎ Jianming Hua, Xiyang Zhia, , Jinnan Gonga, Zhongke Yinb, Zhipeng Fanc a Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China Institute of Remote Sensing Information, Beijing 100192, China c University of Texas at Dallas, Dallas, TX, USA b A R T I C LE I N FO A B S T R A C T Keywords: Satellite vibrations Space-variant image degradation Measurement error Error tolerance Satellite design Satellite vibrations during exposure time could lead to image motion degradation, and image restoration methods are commonly used to compensate for such degradation. However, eﬀects of space-variant image degradation characteristics due to the vibrations for time delayed integration (TDI) camera and real-time measurement errors of the vibration motion are rarely taken into account during the restoration process, which will bring ﬁnal restored image processing error. In this paper, the analytical model of vibration motion is ﬁrst deduced mathematically and then the space-variant modulation transfer function (MTF) degradation and corresponding inﬂuence factors are analyzed. Meanwhile, the eﬀect of measurement errors is theoretically explained on that basis of high-performance restoration model. Then the eﬀects of the space-variant MTF and measurement errors for diﬀerent frequencies, amplitudes and sampling rate on image restoration performance are further presented. Finally, inﬂuences of above factors aﬀecting restoration quality are veriﬁed and the relationships between them are established experimentally. Subsequently, the error tolerance of satellite vibration itself and measurement speciﬁcations are quantitatively generated from the practical application point of view, which can provide a valuable reference for future satellite platform design and the speciﬁcations determining of TDICCD camera. 1. Introduction Nowadays, optical remote sensing satellite images play an increasingly important role in military and civilian ﬁelds, particularly highresolution images, and new requirements are also put forward for the interpretation accuracy of high-resolution images. However, it is diﬃcult to avoid platform vibration during satellite imaging process completely, and for the on-board time delayed integration (TDI) camera, satellite platform vibrations during exposure time not only cause motion blur, but also lead to irregular sampling on the image plane, resulting in geometric quality degradation [1]. Furthermore, with an increasing of image resolution, the impact of the same degree of vibration will be signiﬁcantly enlarged, which seriously aﬀects the interpretation precision of satellite images [2–4]. Consequently, considering that the performance of vibration isolator or gyro-stabilized camera platform is limited by current manufacturing technology, development cost and cycle, image restoration methods are usually adopted to compensate for such motion degradation. In previous studies, lots of restoration methods have been proposed ⁎ to deal with both image deblurring [5] and geometric distortion correction [6], such as total variation regularization [7,8], processing in wavelet domain [9], sparse representation [10]. Despite the fact that they could be very eﬀective in improving image quality such as modulation transfer function (MTF) improvement, noise suppression and image details preserving [11,12], the restoration process is usually regarded as a space-invariant process, consequently, spatial variance of the original image MTF owing to satellite vibration characteristics such as frequency, amplitude as well as TDI Stage is rarely taken into account. Furthermore, they consider little on the eﬀect of processing performance due to the vibration measurement errors that determine the accuracy of input parameters. With the improvement of image resolution, the demand for restoration quality is in urgent need, therefore it is worth carrying on research to analyze the error tolerance of satellite vibration characteristics and measurement error for TDICCD image restoration, providing suggestions for vibration suppression, measurement and ground image processing. Compared with the previous studies in the literature, the physicsbased factors related to the satellite vibrations impacting image Corresponding author. E-mail address: zhixiyang@hit.edu.cn (X. Zhi). https://doi.org/10.1016/j.infrared.2018.08.012 Received 23 April 2018; Received in revised form 24 July 2018; Accepted 12 August 2018 Available online 12 August 2018 1350-4495/ © 2018 Elsevier B.V. All rights reserved. Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. Fig. 1. Restoration results with space-invariant and space-variant MTF: (a) original Image, (b) space-invariant MTF, (c) Degraded Image with MTF in (b), (d) Restored Image of (c), (e) space-variant MTF, (f) Degraded Image with MTF in (e), (g) Restored Image of (f). 2. Theoretical error analysis of TDICCD image restoration caused by satellite vibrations restoration quality and their relationship are analyzed, and the error tolerance with geometric distortion less than 0.1 pixel and Structural Similarity index between the restored and ideal images over 0.9 is discussed, which can provide a valuable and scientiﬁc reference for satellite system design and in-orbit image applications. The rest of this paper is organized as follows. Section 2 presents the theoretical analysis of degradation and restoration process of high resolution TDICCD imagery, and then the image restoration processing error caused by the platform vibration characteristics itself and the vibration measurement error are analyzed in Section 3. In Section 4, the maximum error tolerance of the above inﬂuence factors is studied quantitatively. Subsequently, suggestions of satellite vibration platform are proposed based on the semi-physical experimental results. Finally, we come to a conclusion in Section 5. In this Section, the models of TDICCD image degradation and restoration caused by satellite vibrations are ﬁrst deduced mathematically, on this basis, two key factors having an adverse impact on the restoration quality are discussed, which can provide a theoretical basis for the analysis of inﬂuence factors on restoration quality in Section 3 as well as experimental design in Section 4. 2.1. Space-variant image degradation caused by satellite vibration characteristics Satellite vibrations generally result from changes in-orbit attitude, detector motion or imbalances of related components such as solar array, antenna, etc. [13–15]. Obviously, vibrations could cause disturbance to sampling positions, which may change over time during the imaging process. Although the measured vibration pattern may be 278 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. Fig. 2. Degraded image and corresponding MTF in diﬀerent vibration frequencies: (a) original image, (b) fk = 0.1fes (fk is vibration frequency, fes is sample frequency), (c) Calculated MTF of (b), (d) fk = 0.35fes, (e) Calculated MTF of (d), (f) fk = 4.23fes (g) calculated MTF of (d). 279 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. f=400Hz f=200Hz f=100Hz i+N x¯i = i+N ∑ ∑ x¯k,i,n = ∑ ∑ n=i n=i k k Ak fes ⎡ 2π ⎤ cos(φk, i, n )−cos ⎜⎛ ·fk + φk, i, n⎟⎞ ⎥ 2πfk ⎢ ⎝ fes ⎠⎦ ⎣ (4) As can be seen from Eq. (4), when x̄ i ≠ 0 , it represents distortion occurs in i-th row of acquired image. Obviously, image motion apparently aﬀects grayscale distribution, and moreover, it leads to motion blur in this case. Consider that the well-studied vibration blur can be expressed as: LSFX = Measuring Measuring point one point two Measuring point three Measuring Measuring point four point five Fig. 3. Position of measuring points. complex due to collective eﬀects of its sources, it can usually be decomposed to the summation of several sinusoidal vibration components. And the vibration disturbance resulting from one component can be expressed as follow: = 1 Tes ∫0 Tes In previous work of Yaroslavsky [16] and Zhi [17], etc, an image restoration model of vibration-aﬀected imaging process was proposed: (1) xk, i, j, n (t ) dt = 1 Tes ∫0 Tes g = SHu + n ⎟ 2π Ak Tk ⎡ cos(φk, i, j, n )−cos ⎛ ·Tes + φk, i, j, n⎞ ⎤ 2πTes ⎢ ⎝ Tk ⎠⎥ ⎦ ⎣ ⎜ ⎟ (2) ̂ g||2 } u ̂ = argmin{||u ||̂ 2 + λ||SHu − where (i, j ) is pixel coordinate in the image plane, Tes is the single stage integration time, Ak , Tk and φk, i, j, n denote vibration amplitude, period and phase of k-th component respectively, among which φk, i, j, n is also related to pixel coordinate and stage number n . Since the sensors’ movements of the same CCD stage are identical, we assume that the eﬀect of vibrations along j direction is constant, and omit subscript j for simplicity. From Eq. (2), thus the image motion of n-th stage can be derived as: x¯i, n = 2π A T k k⎡ cos(φk, i, n )−cos ⎛ ∑ x¯k,i,n = ∑ 2πT ⎢ T ⎜ k k es ⎣ ⎝ k ·Tes + φk, i, n⎞ ⎤ ⎠⎥ ⎦ (6) where g is the degraded image, u is the original image, S is a resampling matrix which represents geometric distortion caused by vibrations, H is a blurring operator, which is the inverse fourier transform of MTF, and n is noise. The model can describe not only image blurring induced in the whole physics-based imaging process, but also geometric distortion owning to irregular sampling. Based on regularization methods [8,18], the restoration problem can be expressed as follow: 2π Ak sin ⎛ ·t + φk, i, j, n ⎞ dt ⎝ Tk ⎠ ⎜ (5) 2.2. Eﬀects of vibration measurement errors on image restoration quality where A , T , and φ0 denote vibration amplitude, period and phase respectively. Consequently, for the n-th stage of TDICCD, the image motion, which corresponds to k-th vibration component, can be described as follow: x¯k, i, j, n = δ (X −x (t )) dt es By applying numerical calculation to Eq. (5), the image MTF disturbed by vibrations can be obtained with Fourier transform. Combined with the above formulas, it is clear that the image motion caused by vibration in the integral time will not only cause the image blurring, but also the position deviation of the integral pixels in each row, which leads to space-variant MTF degradation of the TDICCD image consequently. Measuring point six 2π x (t ) = A sin ⎛ ·t + φ0⎞ ⎠ ⎝T (i + N − 1) Tes ∫(i−1) T û (7) where λ is the Lagrange multiplier. Instead of solving Eq. (7) directly, it could be more convenient by using conjugate gradient method, and then the ideal image can be obtained by applying the inverse FFT to u .̂ In order to realize factors having an adverse impact on the restoration quality, a high-performance algorithm is then ﬁxed based on the theoretical methods in Eq. (7), which can implement image deblurring and geometric distortion correction simultaneously. Furthermore, the restoration solution can be obtained within seconds, which means the algorithm can restore high-resolution images eﬀectively with reasonable time. Consequently, in view of the excellent eﬃciency and real-time performance, analyses and experiments in the following ⎟ (3) Summing up image motion results of all stages, assume the total stage number is N, then the overall image motion is obtained as: Fig. 4. Calculated results based on the actual and measured parameters: (a) MTF comparison, (b) Calculation geometric distortion comparison. 280 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. Fig. 5. Restoration results based on the actual parameters and measured ones, (a) restored image based on actual parameters, (b) restored image based on measured parameters. Fig. 6. Calculated MTF and restored images based on the actual parameters and measured ones: (a) p = 0.05 pixel, (b) restored images based on the actual parameters with p = 0.05 pixel, (c) restored images based on the measured parameters with p = 0.05 pixel, (d) p = 0.5 pixel, (e) restored images based on the actual parameters with p = 0.5 pixel, (f) restored images based on the measured parameters with p = 0.5 pixel. MTF and vibration measurement error should be carried out. Sections are based on this algorithm. From the formula derivation in Section 2.1, it can be noticed that considering the image MTF as a space invariant operator is not very accurate. Indeed, it can be more serious owing to vibrations with higher frequency and larger amplitude. Furthermore, as can be seen from the restoration model, both calculations of S and H require high-accuracy measurement of image motion. But limited to the current technological level, vibration measurement error is inevitable. And when it goes beyond a certain tolerance during restoration process, serious artifacts can be obviously realized near the nonsmooth region of the image (such as edges and textures). Consequently, in order to ensure accuracy of restoration model input parameters, further analysis of space variance of 3. Eﬀects of vibration characteristics and measurement errors on image restoration quality 3.1. Eﬀect of space-variant MTF for diﬀerent frequencies and amplitudes on restoration quality In order to illustrate eﬀect of the space-variant MTF on restoration quality, a space-invariant and a space-variant MTF are added to the same scene image respectively, and then images are restored by the high-performance algorithm mentioned in Section 2.2. The restoration 281 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. Degradation Simulation Amplitude Frequency TDI Stage Integration Time High Resolution WorldView-3 Images Harbour Airport City Parameter Calculation and Image Restoration Geometric Distortion Amount PSF Restored Image OTF Data Fitting Image Degradation Simulation Degraded Image Image Quality Assessment and Quantitative Analysis SSIM Vibration Measurement Simulation Actual Image Shift Quantitative Relation Measured Vibration Characteristics Measurement Error Residual Geometric Distortion Fig. 7. Experimental design. Fig. 8. Standard scene images. In order to illustrate space variance of the image MTF, assume the amplitude is 1 pixel and TDI stage is 64, we take vibration frequency as control variable. Fig. 2(b), (d) and (f) show degraded image examples under diﬀerent vibration frequencies. Moreover, as shown in Fig. 2(c), (e) and (g), in each subimage two curves are calculated in reference with diﬀerent columns. As shown in Fig. 2, one can easily notice that the MTF curves of two regions show variations with the changing of vibration frequency, which illustrates the space-variant characteristic of the imaging degradation. Therefore, when the TDI Camera series is ﬁxed, frequency and amplitude are the main factors for space-variant MTF, clearly resulting in inaccurate input for restoration process. In order to successfully implement image restoration and have an excellent application value, space-variance caused by vibration must be restrained, in other words, frequency and amplitude should be controlled in a certain range. result comparison with diﬀerent MTF is shown in Fig. 1, in which (a) is the original image, (c) and (f) illustrate degraded images while the former has a space-invariant MTF, (d) and (g) show corresponding restored images. Through the visual eﬀect of restored images, it can be easily observed that restored image quality with a space-invariant MTF is close to the original image, nevertheless, when the MTF is spacevariant, the detail distortion and edge artifacts are obvious in restored image. Based on existing literature [19,20], when TDI series is certain, it is stated that the MTF calculation method for low frequency vibration can be approximately expressed as: ML (f ) = |J0 (πfA)| (8) where J0 denotes the Bessel function of the ﬁrst kind. Similarly, the MTF calculation method for high frequency vibration is given: Mh (f ) = |J0 (2πfA)| (9) 282 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. position detecting error caused by acceleration sensor itself. Satellite vibrations have a wide range of frequencies, while sampling rate of vibration detector is usually ﬁxed. If vibration frequency is higher than sampling rate, reconstructed vibration waveform may deviate from the actual waveform, thus aﬀecting restoration consequence. Besides, even the sampling rate is suﬃcient, because of measurement device precision restriction, still, there may be slight variations in image pixel position. The inﬂuence of insuﬃcient sampling rate is analyzed below. Assume that the speed of the vibration measurement is 1 ms per measurement point. When the number of push lines is 512, the single stage integration time is 0.05 ms, thus the time required to complete an image is 25 ms, and there are 25 measuring points in an image. Fig. 3 shows the positions of the measurement point with diﬀerent vibration frequencies within 5 ms. It can be seen that when the vibration frequency is 100 Hz, half of the vibration period is included within 5 ms, in other words, there should be 11 points within the whole vibration cycle. With an increase of frequency, for example, when it is 200 Hz, the corresponding measuring points in vibration period will decrease. Therefore, using a small number of measuring points is diﬃcult to collect the complete vibration image motion, which is bound to bring measurement error. Fig. 4 shows an example of reconstructed waveform with an insuﬃcient sampling rate. It is clear that with a low sampling rate, the reconstructed waveform deviates from the actual one, leading to an inaccurate estimation of distortion amount. The corresponding results based on actual and measured parameters in this case are shown in Fig. 5, which indicate that the error owing to unsuitable sampling rate may lead to ripple distortion at the edge of restored images. As previously discussed, the position detecting error of measurement sensor is also an inﬂuence factor. Current detectors may suppress the detecting error below 0.05 pixel, in addition, implementing data ﬁtting may alleviate the disturbance and make it relatively controllable. However, it can be aﬀected by working condition, resulting in degraded restoration accuracy. In order to specify this statement, Fig. 6 illustrates the comparison between sensor measurement error p = 0.05 pixel and p = 0.5 pixel when A = 1 pixel , f = 200 Hz , n = 4 , Tes = 0.05 ms, sampling rate r = 1000 Hz. As one can easily notice from the restoration results, when p = 0.05 pixel, the overall visual eﬀects of restored images based on actual and measured parameters are basically similar. However, when p = 0.5 pixel, compared with the actual parameters result, the restored image with measured parameters shows the unsatisﬁed eﬀect such as Fig. 9. Semi-physical experiment. Table 1 Experimental parameter ranges. Parameter Range Vibration amplitude Vibration frequency TDI stage Sensor measurement error Measurement sampling speed 0.5–2 pixels 1–1000 Hz 1–64 0.01–0.1 pixel 1 point/ms 3.2. Eﬀect of measurement error on restoration quality As already mentioned, vibrations not only cause motion blur, but also the irregular change of sampling positions. In actual image processing, image restoration requires sampling positions as input for distortion correction and MTF for deblurring. Although both factors can be measured with proper ground targets, the obtained data cannot fully represent the working condition of satellite because vibration is timerelevant and sometimes a random process. Therefore, measurement error is a limiting factor on restoration applications. Actually, measurement error in this case usually results from two aspects, insuﬃcient sampling rate owing to measurement speed and Table 2 Experimental results. Amplitude (Pixel) 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 Frequency (Hz) 100 100 100 150 150 150 200 200 200 100 100 100 150 150 150 200 200 200 TDI Stage 4 32 64 4 32 64 4 32 64 4 32 64 4 32 64 4 32 64 Assessment of degraded image Assessment of restored image Measurement error: 0.05 pixel Measurement error: 0.1 pixel SSIM R es SSIM R es SSIM R es 0.8861 0.9017 0.9235 0.8620 0.8901 0.9212 0.8556 0.8615 0.9011 0.7655 0.8038 0.8452 0.7639 0.8018 0.8420 0.7604 0.7914 0.8411 0.6964 0.3278 0.2410 0.7038 0.4545 0.2781 0.7102 0.5902 0.3051 1.3927 0.7956 0.2919 1.4075 0.9090 0.4362 1.4203 1.1804 0.6102 0.9369 0.9514 0.9801 0.9261 0.9452 0.9792 0.9073 0.9203 0.9558 0.8289 0.8517 0.8994 0.8175 0.8451 0.8870 0.8067 0.8346 0.8813 0.0718 0.0662 0.0529 0.0939 0.0751 0.0672 0.1387 0.1287 0.1088 0.1821 0.1436 0.1246 0.1920 0.1573 0.1286 0.2214 0.1683 0.1332 0.8514 0.8744 0.8993 0.8398 0.8631 0.8837 0.7976 0.8264 0.8607 0.7089 0.7335 0.7541 0.7031 0.7275 0.7486 0.6973 0.7206 0.7369 0.1732 0.1534 0.1158 0.1953 0.1611 0.1236 0.2279 0.1732 0.1277 0.4165 0.3489 0.2689 0.4312 0.3641 0.3058 0.4437 0.3721 0.3214 283 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. degradation level could be seen, providing data to ﬁnd out the error tolerance of vibration parameters. As one can easily observe that changes of amplitude, frequency, TDI stage and measurement error all have an impact on restored image quality. In addition, with further analysis of the assessment results and from the practical application point of view, the following error tolerance requirements could be derived and should be considered in satellite platform design: noise ampliﬁcation and jaggy edge artifact. From the analysis above, it is obvious that insuﬃcient sampling rate owing to measurement speed and sensor detecting error are the main aspects for measurement error, which then results in inaccurate input for restoration process. Therefore, select a suitable vibrations sampling rate and control the sensor measurement error in a speciﬁc range are crucial for restoration process. 4. Experimental results and discussion (1) Measurement error has serious impact on the precision of image restoration. Considering the current need of high-resolution satellite images, in order to make structural similarity value higher than 0.9, the measurement error should be controlled below 0.05 pixel, meanwhile, the maximum applicable vibration amplitude for restoration algorithm should be no more than 1 pixel. (2) In a certain range, the increase of frequency leads to more serious geometric distortion. From the point of restoration accuracy, to satisfy the requirement that the residual geometric distortion is less than 0.1 pixel, the maximum applicable vibration frequency for restoration algorithm is 150 Hz. Therefore, vibrations above 150 Hz should be suppressed. 4.1. Experimental design In this Section, the eﬀect laws proposed in Section 3 are veriﬁed by semi-physical experiment, and the experimental design is shown in Fig. 7. In the experiment, 50 high-resolution satellite images from Worldview-3 are selected as standard target images, which consist of city, airport and harbor as shown in Fig. 8. The image resolution is 0.3 m and geometry correction is applied before the experiment. The semi-physical experiment platform is built in the laboratory, which consists of a high speed camera, a light source, standard target images, a piezoelectric ceramic fast deﬂection mirror and a vibration console as shown in Fig. 9. The standard target image selected as real scene is ﬁxed, and the vibration console is connected with the piezoelectric ceramic fast deﬂection mirror. By adjusting the output waveform of the console, the deﬂection mirror can have impact on the vibration of the experimental optical path. In addition, a high-speed camera is used to capture the target image reﬂected by the deﬂector mirror and collect the vibration information, simulating the imaging process of TDI. Based on the experiment, the images are generated with diﬀerent level of vibration parameters such as frequency and amplitude. Meanwhile, the input parameters for restoration are generated with diﬀerent level of measurement errors. In order to quantify the inﬂuence relation and analyze the error tolerance, as shown in Table 1, experimental parameters are given a research range, respectively. 5. Conclusion In this study, the error tolerance and eﬀects of satellite vibration characteristics and measurement error on TDICCD image restoration are proposed. First, the model of space-variant image MTF containing vibration motion of TDICCD stages is mathematically deduced, and the vibration factors aﬀecting the restoration performance are theoretically proposed combined with high-performance restoration model. Second, eﬀects of vibration characteristics and measurement errors on image restoration quality are proposed through the results of the theoretical analysis. Finally, the eﬀects of above factors aﬀecting restoration quality are veriﬁed and the error tolerance of vibration characteristics and measurement is quantitatively generated by semi-physical experiment. The experimental results demonstrate that when the sampling rate of vibration detector is ﬁxed at 1 point/ms, in order to meet the requirements that residual geometric distortion is less than 0.1 pixel and SSIM value is greater than 0.9, the measurement error of vibration detector should be below 0.05 pixel and the vibrations frequencies higher than 150 Hz should be suppressed, meanwhile, the maximum applicable vibration amplitude for restoration algorithm should be no more than 1 pixel. The analytical method can be applied to improve high-resolution image processing performance and it possesses potential application prospects on the satellite system design and the speciﬁcations determining of TDICCD camera in the remote sensing ﬁeld. 4.2. Evaluation of restoration quality Structural Similarity (SSIM) is a full reference image quality evaluation method [21,22], which takes luminance, contrast and structure information of images into consideration, respectively. The contrast information and the structure information can reﬂect the blur eﬀects and texture preserving performance eﬃciently. Therefore, SSIM is applied here to evaluate the performance of image restoration. In addition, to evaluate the performance of geometric distortion correction, homonymous points of original image and restored image were extracted by high precision Scale-invariant feature transform algorithm (SIFT) [23,24] respectively, and a novel residual geometric distortion metric is given by: Conﬂict of interest n R es = ± We declare that we have no conﬂicts of interest to this work. ∑i = 1 (Δx i )2 + (Δyi )2 n (10) References where Δx i and Δyi denote the coordinate point diﬀerence of corresponding homonymous points from original image and restored image, n denotes the numbers of homonymous points. Based on accurate location coordinate information of homonymous points, the R es can represent the geometric distortion precision correctly. [1] Z.L. Wang, X.X. Zhuang, L.Q. Zhang, Eﬀect of image motion and vibration on image quality of TDICCD camera, Applied Mechanics and Materials, Trans Tech Publications, 2012, pp. 584–588. [2] C. Serief, Estimate of the eﬀect of micro-vibration on the performance of the Algerian satellite (Alsat-1B) imager, Optics Laser Technol. 96 (2017) 147–152. [3] Q. Hu, Input shaping and variable structure control for simultaneous precision positioning and vibration reduction of ﬂexible spacecraft with saturation compensation, J. Sound Vib. 318 (1) (2008) 18–35. [4] C. Brian, Pleiades 1B and SPOT 6 image quality status after commissioning and 1st year in orbit, in: Proceedings of the Joint Agency Commercial Imagery Evaluation (JACIE) Workshop, Louisville, KY, USA, 2014, pp. 26–28. [5] W. Li, R. Chen, S. Xu, et al., Blind motion image deblurring using nonconvex higherorder total variation model, J. Electron. Image. 25 (5) (2016) 053033. [6] M. Alghoniemy, A.H. Tewﬁk, Geometric distortion correction through image normalization, 2000 IEEE International Conference on Multimedia and Expo, 2000. 4.3. Relationship between restoration quality and vibration parameters and their error tolerance In this Section, to quantify the inﬂuence relation and analyze the error tolerance, Table 2 lists a part of the combinations of various inﬂuence parameters and corresponding restoration image assessment results. On this basis, the restoration performance with each 284 Infrared Physics and Technology 93 (2018) 277–285 J. Hu et al. [16] L.P. Yaroslavsky, Compression, restoration, resampling, ‘compressive sensing’: fast transforms in digital imaging, J. Optics 17 (7) (2015). [17] X. Zhi, Q. Hou, X. Sun, et al., Degradation and restoration of high resolution TDICCD imagery due to satellite vibrations, International Symposium on Optoelectronic Technology and Application 2014: Image Processing and Pattern Recognition, International Society for Optics and Photonics, 2014, p. 93012I. [18] X.G. Lv, Y.Z. Song, S.X. Wang, et al., Image restoration with a high-order total variation minimization method, Appl. Mathemat. Model. 37 (16–17) (2013) 8210–8224. [19] A. Stern, N.S. Kopeika, Analytical method to calculate optical transfer functions for image motion and vibrations using moments, JOSA A 14 (2) (1997) 388–396. [20] Y. Du, Y. Ding, Y. Xu, et al., Dynamic modulation transfer function analysis of images blurred by sinusoidal vibration, J. Optical Soc. Korea 20 (6) (2017) 762–769. [21] Y. Ye, J. Shan, L. Bruzzone, et al., Robust registration of multimodal remote sensing images based on structural similarity, IEEE Trans. Geosci. Remote Sens. 55 (5) (2017) 2941–2958. [22] L. Gomez-Chova, D. Tuia, G. Moser, et al., Multimodal classiﬁcation of remote sensing images: a review and future directions, Proc. IEEE 103 (9) (2015) 1560–1584. [23] B. Kupfer, N.S. Netanyahu, I. Shimshoni, An eﬃcient SIFT-based mode-seeking algorithm for sub-pixel registration of remotely sensed images, IEEE Geosci. Remote Sens. Lett. 12 (2) (2015) 379–383. [24] A. Sedaghat, H. Ebadi, Remote sensing image matching based on adaptive binning SIFT descriptor, IEEE Trans. Geosci. Remote Sens. 53 (10) (2015) 5283–5293. ICME 2000, IEEE, 2000, pp. 1291–1294. [7] A. Makovetskii, S. Voronin, V. Kober, Total variation regularization with bounded linear variations, Applications of Digital Image Processing XXXIX, International Society for Optics and Photonics, 2016, p. 99712T. [8] W. He, H. Zhang, L. Zhang, et al., Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration, IEEE Trans. Geosci. Remote Sens. 54 (1) (2016) 178–188. [9] Y. Yang, B. Chen, Image restoration based on wavelets and curvelet, SPIE/COS Photonics Asia, International Society for Optics and Photonics, 2014, pp. 92733I–927339. [10] R.R. Bhawre, Y.S. Ingle, Review on image restoration using group-based sparse representation, 2014 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), IEEE, 2014, pp. 1–4. [11] J. Li, Z. Liu, S. Liu, Suppressing the image smear of the vibration modulation transfer function for remote-sensing optical cameras, Appl. Optics 56 (6) (2017) 1616–1624. [12] D. Wang, T. Zhang, H. Kuang, Clocking smear analysis and reduction for multi phase TDI CCD in remote sensing system, Optics Exp. 19 (6) (2011) 4868–4880. [13] T. Sun, H. Long, B.C. Liu, et al., Application of attitude jitter detection based on short-time asynchronous images and compensation methods for Chinese mapping satellite-1, Optics Exp. 23 (2) (2015) 1395–1410. [14] N. Yi-Bing, T. Yi, Z. Li-Jun, et al., Evaluation of inﬂuences of frequency and amplitude on image degradation caused by satellite vibrations, Chin. Phy. B 24 (5) (2015) 058702. [15] E. Azadi, S.A. Fazelzadeh, M. Azadi, Thermally induced vibrations of smart solar panel in a low-orbit satellite, Adv. Space Res. 59 (6) (2017) 1502–1513. 285

1/--страниц