Spatial resolution enhancement of hyperspectral images based on redundant dictionaries

Transcription

1 Spatia resoution enancement of yperspectra images based on redundant dictionaries Suyu Wang Bo Wang Zongxiang Zang

2 Spatia resoution enancement of yperspectra images based on redundant dictionaries Suyu Wang, a,b, * Bo Wang, a,b and Zongxiang Zang a,b a Beijing University of Tecnoogy, Scoo of Software Engineering, No. 100 Ping Leyuan, Caoyang Disctrict, Beijing , Cina b Beijing Engineering Researc Center for IOT Software and System, No. 100 Ping Leyuan, Caoyang District, Beijing , Cina Abstract. Spatia resoution enancement of yperspectra images is one of te key and difficut topics in te fied of imaging spectrometry. Te redundant dictionary based sparse representation teory is introduced, and a spatia resoution enancement agoritm is proposed. In tis agoritm, a pixe curve instead of a pixe patc is taken as te unit of processing. A pair of ow- and ig-resoution respective redundant dictionaries are joint trained, wit te constraint tat a pair of ig- and ow-resoution corresponded pixe curves can be sparse represented by same coefficients according to te respected dictionaries. In te process of super-resoution restoration, te ow-resoution yperspectra image is first sparse decomposed based on te ow-resoution redundant dictionary and ten te obtained coefficients are used to reconstruct te corresponding ig-resoution image wit respect to te ig-resoution dictionary. Te maximum a posteriori based constrained optimization is performed to furter improve te quaity of te reconstructed ig-frequency information. Experimenta resuts sow tat te pixe curve based sparse representation is more suitabe for a yperspectra image; te igy spectra correations are better used for resoution enancement. In comparison wit te traditiona biinear interpoation metod and oter referenced super-resoution agoritms, te proposed agoritm is superior in bot objective and subjective resuts. Te Autors. Pubised by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of tis work in woe or in part requires fu attribution of te origina pubication, incuding its DOI. [DOI: /1.JRS ] Keywords: yperspectra image; super-resoution restoration; redundant dictionary; sparse decomposition. Paper 14786SS received Dec. 31, 2014; accepted for pubication Ju. 29, 2015; pubised onine Aug. 26, Introduction Hyperspectra imaging is a major breaktroug in te fied of eart observation tat occurred at te end of te ast century. It combines te tecniques of imaging and spectroscopy, fuses te spatia and spectra information of te imaging targets. 1 Wit yperspectra imaging, an observing target can be imaged in dozens to undreds of spectra bands, covering te range from utravioet to microwave, wic far exceed te imit of uman vision. Terefore, it can detect bot spatia and spectra caracteristics of te target, and provide more effective information for anayzing and distinguising te properties. Currenty, appication of yperspectra remote sensing as been extended from te traditiona fieds of miitary reconnaissance and topograpic mapping to urban panning, resources investigation, environmenta monitoring, traffic management, etc. Tus, it is paying a more and more important roe in te fieds of remote sensing and eart observation. Spatia resoution and spectra resoution are te two most important indicators wen measuring te quaity of yperspectra images. Spatia resoution describes te abiity to resove spatia detais in te target tat are being imaged, wie spectra resoution measures te abiity to resove eectromagnetic spectrum features. How to increase bot te spatia and spectra resoutions is a key topic of te yperspectra imaging tecnoogy. However, due to te constraint of *Address a correspondence to: Suyu Wang, E-mai: suyuwang@emais.bjut.edu.cn Journa of Appied Remote Sensing Vo. 9, 2015

3 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... imaging mecanisms, te two goas cannot be acieved simutaneousy. Tis is because te spectra bandwidt of a yperspectra imaging system is very narrow, and tus, a arge fied of view is needed to coect enoug igt quanta to maintain an acceptabe signa-to-noise ratio. 2 Terefore, spectra resoution enancement of a yperspectra image is often at te cost of spatia resoution decreasing. Because of tis, te spatia resoution of yperspectra images is muc ower tan tat of te common visibe or pancromatic images. Fortunatey, super-resoution (SR) restoration, 3,4 a signa processing based resoution enancement metod, provides a new coice to resove tis probem witout any ardware costs. Tis tecnique as been widey investigated for visibe images/videos. However, few of tem were speciay designed for yperspectra images. In most cases, a yperspectra image was taken as a sequence of gray images wit somewat compementary information between eac band and ten was reconstructed by traditiona SR metods band by band. 5 However, yperspectra images are quite different from visibe images. One of te most significant caracteristics is tat it as muc iger spectra correations tan oter image sequences, wie te spatia correations are quite ow. Traditiona spatia based SR metods may not acieve as good performance as for visibe images. In addition, SR agoritms are often computation-intensive and time-consuming, wen appied to dozens of yperspectra bands separatey, te computations tat required were unbearabe. In te fied of visibe image SR, a sparse representation based agoritm 6 as sown good performance. However, for te aforementioned reasons, it is not suitabe to be directy used for yperspectra images. On te oter and, a pixe curve based sparse metod as been proven effective for describing yperspectra images and as sown good performances in spectra unmixing and cassification appications,butfewforsr.intispaper,tesparse representation based SR metod 6 is speciay investigated for yperspectra images and a redundant dictionary based yperspectra image SR restoration agoritm is proposed. According to te specific caracteristics of te yperspectra images, te pixe curve (formed by te pixes ocated on te same coordinate point troug te bands) instead of te pixe patc is considered as an atom of te dictionary. During te process of dictionary training, a pair of ig resoution (HR) and ow resoution (LR) corresponding training sets are created by pixe curves from HR yperspectra images and teir simuated degraded images. Ten te dictionary pair is jointy trained from te set of pixe curves wit te constraint tat wen a pixe curve from te HR yperspectra image and its degraded image is decomposed according to te HR and LR dictionary pair, respectivey, we can get te same sparse coefficients. In te process of SR restoration, eac pixe curve from te LR yperspectra image wi first be decomposed according to te LR dictionary of te dictionary pair to obtain a set of sparse coefficients, ten te corresponding HR curve is reconstructed by te LR coefficients and te HR dictionary. Wen a te curves are SR reconstructed, a te bands of te estimated HR image are optimized by a maximum a prior (MAP) based agoritm to furter improve te quaity. In tis agoritm, te yperspectra images are sparsey decomposed as a woe for eac pixe on te spectra dimension. In tis way, te pixe curves are regarded as a unit during te entire process; spectra features tat are often described by te curves are effectivey preserved. Te pixe curve based sparse representation is more suitabe for yperspectra images in order to make better use of its ig spectra correations. At te same time, as te number of bands (corresponding to number of vaues in a pixe curve) is often arger tan te number of pixes in te traditiona image patces, te tota computation is aso saved. Te experimenta resuts are compared wit te foowing reated agoritms incuding biinear interpoation, MAP based SR, and te traditiona pixe patc based sparse SR metod. Te proposed agoritm is superior in bot objective and subjective resuts. Te structure of tis paper is as foows. In Sec. 2, te reated background of te proposed agoritm and te framework of te agoritm are introduced. In Sec. 3, te basic principe of yperspectra image sparse decomposition is described. Te core of te proposed agoritm is eaborated in Sec. 4, tat is, te design and training process of te redundant dictionary pair. In Sec. 5, te process of te HR yperspectra images reconstruction is presented. In Sec. 6, experimenta resuts of te agoritm are given and te vaidity of te agoritm is verified. Journa of Appied Remote Sensing Vo. 9, 2015

4 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... 2 Agoritm Outine 2.1 Reated Background Redundant dictionary based sparse decomposition is a new kind of signa representation metod 1 tat was proposed in te 1990s. It as canged te traditiona idea of ortogona basis based metods, in tat te traditiona ortogona basis was substituted by te redundant dictionary, wic consisted of a set of overcompete functions. Te dictionary was caed redundant because it consisted of severa basis functions to be used seectivey. In te decomposition process, te best basis functions were seected according to te caracteristics of a certain signa in order to represent it more effectivey. In tis way, sparser representation coefficients may be obtained by seecting a set of more suitabe bases. Neuroogica researces ave sown tat overcompete representation was more compiant wit te bioogy of a mamma s visua system. 7 Moreover, noninear approximation teory aso proved tat te approximation of an overcompete system was superior to te known ortogona basis. In te fied of image processing, te overcompete sparse representation metod as sown better resuts in denoising, restoration, and segmentation appications. It aso brougt significant improvements to compression and equaization appications. 8 In te fied of yperspectra images anaysis, te sparse based metod was designed in a pixe curve based way. For exampe, an unsupervised earning based sparse coding metod was improved for yperspectra images in Ref. 9. Experimenta resuts sowed tat te redundant dictionary created by earning coud describe te spectra features of yperspectra images better tan ortogona transform based ones, tus coding te features of te images in a sparser way. Moreover, wen te sparse coding metod was used for cassification, bot te compexity of te cassifier and number of required sampes were decreased. A spectra unmixing metod for a yperspectra image based on sparse decomposition was proposed in Ref. 10. Te redundant dictionary was trained by te spectra ibrary sampes, dependence on end member extraction accuracy, as done by oter agoritms was avoided, and good resuts were obtained. Te researces mentioned above indicated tat te features in te yperspectra images coud be better described wit ess data by redundant dictionary based sparse representation metods. In tis paper, te sparse representation based visibe image SR agoritm 6 is improved for yperspectra images. A redundant dictionary based yperspectra image SR restoration agoritm is proposed. By using of more effective redundant dictionary based yperpsectra image representation metod, better performance as been acieved. 2.2 Agoritm Framework Te bock diagram of te proposed redundant dictionary based SR restoration agoritm for yperspectra images is sown in Fig. 1. In tis agoritm, a pair of HR and LR corresponding redundant dictionaries is precreated by joint earning, wit te constraint tat te respective HR and LR pixe curves woud ave te same sparse representation coefficients wen decomposed according to te respective dictionaries. Wen turning to SR restoration, te input LR yperspectra image is first biineary interpoated to te expected resoution so as to ave te same Fig. 1 Bock diagram of te proposed agoritm. Journa of Appied Remote Sensing Vo. 9, 2015

5 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... number of spectra curves as te HR images. Furtermore, eac pixe curve in te interpoated LR images is sparsey decomposed based on te LR redundant dictionary of te dictionary pair. Ten te HR yperspectra image is reconstructed by using te obtained sparse representation coefficients and te corresponding HR redundant dictionary. Finay, eac band of te reconstructed primary HR image is optimized by te MAP based metod to furter improve te performance. 3 Principe of Pixe Curve Based Sparse Decomposition of te Hyperspectra Image Hyperspecstra image is a kind of image tat can image a target to dozens of bands. For a certain target materia to be imaged, a te pixes ocated on te same coordinate point troug te bands form a curve, named te spectra curve. Tis curve refects te spectra features of te imaged materia. Any materia as its own spectra curves, and simiar materias ave simiar ones. In appications, any pixe curve in te image is reated to te target materia s spectra curve or can be considered as a combination of severa spectra curves, wen te target area is reated to severa kinds of materias. Tat is simiar to te ways tat te redundant dictionary based metod do. Te most typica pixe curves were seected by training and were considered as atoms of te redundant dictionary. Tus, any pixe curve can be represented by a combination of severa atoms. Some researces 10 suggested tat by redundant dictionary based sparse decomposition, te atoms of te trained redundant dictionary refected te spectra features of te imaging materias. Most of te atoms were consistent wit a certain spectra curve of te materia. Te creation of te redundant dictionary is te core of te agoritm. Currenty, te mainstream metod is based on earning, a te atoms of te dictionary are generated by training of te data. Tat is to say, te most representative eements are seected from a arge number of training sampes, ten tey are taken as te atoms to constitute te redundant dictionary. In tis way, any pixe curve can be described in te manner of an optima inear combination of te atoms. For exampe, te metod of optima direction, 11 te generaized principa component anaysis metod, 12 te metod of kerne singuar vaue decomposition (K-SVD), 9,13 and te metod of sparse dictionary earning 12 are a typica metods for dictionary training. In tis study, te metod of K-SVD is used. K-SVD 13 is a dictionary earning agoritm via an SVD approac. It is a generaization of te k-means custering metod and works by iterativey aternating between sparse coding te input data based on te current dictionary and ten updating te atoms in te dictionary to better fit te data. Te goa of te agoritm is to resove te optimization probem of Eq. (1). EQ-TARGET;temp:intraink-;e001;116;308min kx D;C DCk2 2 ; subject to i; kc i k 0 T 0 ; (1) were D is te dictionary created troug training and X is te set of training pixe curves. C is te coefficient matrix of te sparse representation for pixe curves X, and T 0 is te subjective assumption of sparsity satisfying T 0 < K, were K is te number of atoms in te dictionary. As presented in Ref. 13, tis probem can be resoved by aternative optimization of te dictionary D and te coefficients C. Tat is, first assuming tat D is fixed, pursue te optima representation vectors c i by soving te foowing equation: EQ-TARGET;temp:intraink-;e002;116;200c i ¼ arg minkx i Dc i k 2 c 2 ; st; kc ik 0 < T 0 : (2) i Ten update te dictionary by minimizing te overa representation error. EQ-TARGET;temp:intraink-;e003;116;158E k ¼ X X d j c j T : (3) j k As a metod for dictionary training, te input mutidimensiona signa can be represented in te sparse inear form of te atoms in te dictionary by using te K-SVD agoritm. Te atoms obtained troug training are usuay independent, but are not necessariy ineary uncorreated. For te yperspectra image, eac atom obtained troug training usuay represents te spectra curve of a certain ground materia tat is imaged by te spectrometer. Moreover, any pixe curve Journa of Appied Remote Sensing Vo. 9, 2015

6 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... of te image is te imaging resut of a singe materia or a mixture of severa ground materias. Terefore, te pixe curves can be decomposed into a inear combination of severa atoms. In practica appications, st; kc i k 0 < T 0 is usuay substituted by st: min kc 1 k to simpify te soution process of Eq. (2). Tus, te probem above is sovabe witout subjective estimation of T 0. Moreover, c i is normaized to satisfy 0 c i 1. Te foowing can be obtained by merging te objective functions: EQ-TARGET;temp:intraink-;e004;116;663c ¼ arg min kx Dck 2 2 þ λ kck 1; (4) were x R p, c R K, D R p K, and λ is te equiibrium factor wic is used to equiibrate te weigt between te convergence precision and sparsity of sparse representation. In genera, according to experience, good resuts can be obtained wen λ ¼ Training and Creation of te Redundant Dictionary Pair Te training metod for te LR and HR corresponding redundant dictionary pair is designed on te basis of te K-SVD based redundant dictionary training agoritm, as sown in Fig. 2. In te diagram, te degradation mode of te yperspectra image is first created according to te imaging principe and te degradation process of yperspectra images, and is usuay composed of te stages of subsamping and burring. Te training data are created as foows: first, a group of HR yperspectra images expected to contain sufficient spectra features are seected. Ten te corresponding LR images are generated by first appying te degradation mode to te HR images and ten biineary interpoating to regain te origina number of pixe curves. Tat is to say, te LR image as te same number of pixe curves as te origina HR images. Te ony difference is tat it carries ess ig-frequency information because of te oss during te sub and upsampe processes. During te training process, te HR and LR corresponding pixe curves from te respective images are used to construct te dictionary pair. Te HR yperspectra image is denoted by X, and te corresponding LR image is X. Hence, te corresponding HR and LR dictionaries can be obtained by minimizing te foowing objective equation: EQ-TARGET;temp:intraink-;e005;116;385fD ;D ; Λ g¼arg min fkx D Λk 2 2 þkx D Λk 2 2 þ λkλk 1g; (5) D ;D ;Λ were Λ is te vector consisting of te sparse coefficients α. Troug training, D and D are te obtained optima redundant dictionary pair, respectivey. λkλk 1 is a normaization item for soving te above optimization probem. In te optimization procedure, te HR and LR sparse coefficients are jointy designed. Tat is to say, coefficients of an HR pixe curve based on te HR dictionary are enforced to be simiar to tat of te LR pixe curves based on te LR dictionary. Terefore, in te SR restoration process, te HR image can be reconstructed by using te coefficients obtained by te LR pixe curve and te corresponding HR redundant dictionary. Fig. 2 Diagram of te design process of te redundant dictionary pair. Journa of Appied Remote Sensing Vo. 9, 2015

7 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... 5 Super-Resoution Reconstruction of Hyperspectra Images Wen te HR and LR corresponding redundant dictionary pair is created, for any pixe curve x i in te LR yperspectra image, its sparse representation coefficients can be obtained troug Eq. (6). EQ-TARGET;temp:intraink-;e006;116;680α ¼ arg minfkx i α D αk 2 2 þ λkαk 1g: (6) Ten te estimated HR pixe curve ^x can be reconstructed according to Eq. (7). EQ-TARGET;temp:intraink-;e007;116;632^x i ¼ D α ; (7) were D and D are te pair of HR and LR corresponding redundant dictionaries. In te proposed pixe curve based manner, te pixe curve is considered as a unit during te woe process of decomposition and reconstruction. Spectra compementary information is fuy used for resoution enancement. However, te spatia correation, atoug muc ower tan in common images, may aso contribute to te SR work. Tus eac band of te reconstructed HR image is furter optimized by te MAP based agoritm. Under te framework of MAP probabiity, eac band of te reconstructed HR image soud satisfy EQ-TARGET;temp:intraink-;e008;116;516^b ðjþ ¼ arg max og Prðb ðjþ jbðjþ Þ¼arg maxfog Prðb ðjþ Þþog PrðbðjÞ jb ðjþ Þg: (8) Here, to distinguis from te pixe curves denoted by x ðiþ and x ðiþ, respectivey, b ðjþ and b ðjþ are used for denoting te respective HR and LR image bands j. Prðb ðjþ Þ is a posteriori probabiity of te HR band b ðjþ wen te LR band bðjþ is known. Prðb ðjþ jbðjþ Þ is te priori distribution of te HR band, described by te Huber-Markov mode. 14 Conditiona probabiity Prðb ðjþ jb ðjþ refects te distribution of error between te LR estimate band obtained after te subsamping of ^b ðjþ and te actua LR band b ðjþ. It is considered to obey Gaussian distribution. EQ-TARGET;temp:intraink-;e009;116;393Prðb ðjþ jb ðjþ Þ¼ 1 2π N 1 N 2 exp 2 σ ðjþn 1N 2 Þ 1 kb ðjþ 2σ ðjþ2 Db ðjþ ; k2 (9) were M and N are te number of pixes in te row and coumn of LR band b ðjþ, respectivey. σ ðjþ is te variance of error distribution of te j t band. D is te subsamping matrix. Eac band of te HR image obtained by te above sparse based metod is te initia vaue of b j. By soving Eq. (8) iterativey, te estimated HR band of te image is obtained. During te iteration, te LR mode constraint 15 is empoyed for eac iteration resut. Tus, te stabiity of te agoritm can be furter promoted. 6 Experimenta Resut and Anaysis Te test data are a set of 128-band yperspectra images coected by te OMIS image spectrometer. One of tem named OMISr02, wic contains most of te imaged materias, is seected as te training data. Te spatia resoution of te training data is pixes. Te 113t band of te image, wic corresponds to te visibe range, is sown in Fig. 3. Te test data incude te training image r02 and anoter group of test images, r01 and r Visibe Bands Tests First, te 113t bands of OMISr02 and OMISr03 are used to evauate te performance on visibe images. Comparison of te experimenta resuts are sown in Fig. 4, were te image OMISr03 is divided into four pieces to sow more detais. Te comparing agoritms incude biinear interpoation, a traditiona MAP based visibe image SR metod proposed in Ref. 14, and te sparse based SR metod proposed in Ref. 6. In tis experiment, te SR scae is set to Journa of Appied Remote Sensing Vo. 9, 2015

8 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... Fig. 3 Te 113t band of te training image OMISr02. Fig. 4 Subjective comparison of te experimenta resuts (band 113): (a) te origina igresoution image, (b) biinear interpoation, (c) te sparse based metod, 6 (d) te maximum a prior based aogritm, 14 and (e) te proposed agoritm. 2 2, wic means tat bot te vertica and orizonta resoutions of te image are ampified by 2. As sown in Fig. 4, te first coumn is te 113t band of te origina HR images. Te second coumn sows resuts from te biinear interpoation of te LR images. Te tird and fourt Journa of Appied Remote Sensing Vo. 9, 2015

9 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... Tabe 1 113t band peak signa-to-noise ratio (PSNR) vaue comparison. Test image Biinear Sparse 6 Maximum a prior 14 Proposed OMISr02_ OMISr03_113_a OMISr03_113_b OMISr03_113_c OMISr03_113_d Average coumns are te reconstruction resuts from te sparse based metod proposed in Ref. 6 and te MAP based agoritm proposed in Ref. 14, respectivey, and te ast coumn sows resuts from te metod proposed in tis paper. It can be seen from te resuts tat for eiter te training data or te test data, te quaity of te reconstructed images by te proposed agoritm is better tan tat of te oter agoritms. Te texture structures in te images are muc cearer. Te comparison of PSNR vaues of te 113 bands of te image is furter sown in Tabe 1. It can be seen tat for bot te training image (r02) and te test images (r03_a to r03_d), te resuts of reconstruction by te proposed metod are better tan tose by te oter agoritms, and te PSNR vaues are significanty increased. 6.2 A Bands Test To evauate te performances toug a te spectra bands, more bands of te test images are used in te foowing experiment. Te comparison of PSNR vaues is sown in Tabe 2. Here te SR factor is set to 4 4. Considering tat te MAP based metod is time-consuming and too muc time is required wen it is appied for a te bands, in tis experiment ony te sparse Tabe 2 A bands PSNR vaue comparison. Test image Biinear interpoation Sparse based agoritm 6 Proposed agoritm OMISr01_av OMISr01_ OMISr01_ OMISr01_ OMISr01_ OMISr02_ OMISr02_ OMISr02_ OMISr02_ OMISr03_ OMISr03_ OMISr03_ OMISr03_ Average Journa of Appied Remote Sensing Vo. 9, 2015

10 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra... Tabe 3 Time consumption comparison. Stage Sparse based agoritm 6 (s) Proposed agoritm (s) Improvement (%) Dictionary training 19, , Sparse decomposition 24, Super-resoution reconstruction based agoritm is compared wit te proposed one. Te first ine of Tabe 2 sows an average PSNR vaue of a te 128 bands of OMISr01, and te foowing are severa singe bands of te test images. Te average PSNR vaue of te isted bands is given in te ast ine. It can be seen from te resuts tat for any band of te image, te PSNR vaues are significanty increased. At ast, time consumption of te agoritm wen appied to a bands of OMISr01 is isted in Tabe 3. It can be seen tat for any stage of te agoritm, ess time is required for te proposed agoritm. For te sparse decomposition and SR reconstruction period steps, te time required is decreased by more tan 60% and 40%, respectivey. Tis is very important because te decomposition and reconstruction operations are needed during te woe process of super resoution. So efficiency improvements of tese two stages are far more meaningfu in practica appications. Moreover, it can be seen from a te above experimenta resuts tat tere is no obvious difference between te resuts of te training data (OMISr02) and test data (OMISr01 and OMISr03). Tat is to say, for a certain yperspectra imaging device, wen te redundant dictionary pair is trained by a set of images tat contain most of te imaged materias, it can be used for oter images coected by te same device. So te dictionary pair can be trained beforeand and can be generay used for oter appications. Tat wi furter reduce te computing burden of training te dictionaries. 7 Concusion In tis paper, a redundant dictionary based yperspectra image SR restoration agoritm is proposed. Tis proposed metod takes fu advantage of bot spectra and spatia information to enance te spatia resoution of te yperspectra images. A sparse representation based SR metod is speciay redesigned by using pixe curves instead of patces as te processing units. In tis manner, spectra correations of te image are better used for resoution enancement. Moreover, a MAP based spatia SR metod is used band by band to take furter advantage of te spatia information. Experimenta resuts sow our metod s superior performance compared to oter simiar agoritms. Not ony te objective and subjective quaities of te reconstructed images are obviousy improved, but te time required is reduced. Acknowedgments Tis work is supported by te Nationa Natura Science Foundation of Cina (No ), Science Foundation of te Beijing Education Commission (KM ), Training Programme Foundation for te Taents in Beijing City (2013D ), and Training Programme Foundation for te Yout Taents by Beijing Education Commission. References 1. L. P. Zang, Hyperspectra Remote Sensing, Wuan University Press, Wuan (2005). 2. L. Jifan et a., A yperspectra imager wit adjustabe spectra seectivity based on AOTF, Proc. SPIE 7857, 78571K (2010). 3. Z. W. Lu et a., Overview on image super resoution reconstruction, in Te 26t Cinese Contro and Decision Conf., pp , IEEE (2014). Journa of Appied Remote Sensing Vo. 9, 2015

11 Wang, Wang, and Zang: Spatia resoution enancement of yperspectra W. C. Siu, Review of image interpoation and super resoution, in Asia-Pacific Signa & Information Processing Association Annua Summit and Conf., pp. 1 10, IEEE (2014). 5. G. A. Licciardi, Fusion of yperspectra and pancromatic images: a ybrid use of indusion and noninear PCA, in Proceedings of t IEEE Int. Conf. on Image Processing (ICIP), pp , IEEE (2012). 6. J. Yang, Image super resoution via sparse representation, IEEE Trans. Image Process. 19, (2010). 7. B. A. Osausen and D. J. Fied, Sparse coding wit an overcompete basis set: a strategy empoyed by V1[J], Vision Researc 37(23), (1997). 8. D. H. Liu, G. M. Si, and D. A. Gao, A new metod for signa sparse decomposition, in IEEE Int. Symp. on Inteigent Signa Processing and Communication Systems, pp , IEEE (2007). 9. A. S. Cares, B. A. Osausen, and C. J. Roze, Learning sparse codes for yperspectra imagery, IEEE J. Se. Topics Signa Process. 05, (2011). 10. M. D. Iordace, A. Paza, and J. Bioucas-Dias, Recent deveopment in sparse yperspectra unmixing, in IEEE Int. Symp. on Geoscience and Remote Sensing, pp , IEEE (2010). 11. J. K. Engan and S. O. Aase, Metod of optima directions for frame design, in IEEE int. Conf. on Acoustics, Speec and Signa Processing, Vo. 04, pp (1999). 12. M. R. Rubinstein and A. M. Bruckstein, Doube sparsity: earning sparse dictionaries for sparse signa approximation, IEEE Trans. Signa Process. 58, (2010). 13. M. Aaron, M. Ead, and A. Bruckstein, K-SVD an agoritm for designing of overcompete dictionaries for sparse representation, IEEE Trans. Signa Process. 54(11), (2006). 14. R. R. Scutz and R. L. Ricard, Extraction of ig-resoution frames from video sequence, IEEE Trans. Image Process. 05, (1996). 15. L. Zuo, S. Wang, and X. Li, Image/Video Superresoution, 1 ed., Posts & Teecom Press, Beijing (2011). Suyu Wang is an associate professor of Beijing University of Tecnoogy. Se received er MS degree in communication and information systems from Sicuan University in 2002 and er PD in pattern recognition and inteigent systems from te Beijing University of Tecnoogy in Se is te autor of more tan 30 journa papers and as written four book capters. Her current researc interests incude yperspectra image processing, image/video processing, etc. Bo Wang is a postgraduate student of Beijing University of Tecnoogy, majoring in software engineering. His current researc interest is sparse based yperspectra image processing. Zongxiang Zang is a postgraduate student of Beijing University of Tecnoogy, majoring in software engineering. His current researc interest is sparse based yperspectra image super resoution reconstruction. Journa of Appied Remote Sensing Vo. 9, 2015