Quality Assessment of Restored Satellite Data. Based on Signal to Noise Ratio

Transcription

1 Appled Mathematcal Scences, Vol. 0, 06, no. 49, IKARI Ltd, ualty Assessment of Restored Satellte Data Based on Sgnal to Nose Rato Asmala Ahmad Department of Industral Computng Faculty of Informaton and Communcaton Technology Unerst Teknkal Malaysa Melaka Melaka, Malaysa Shaun uegan Department of Appled Mathematcs School of Mathematcs and Statstcs Unersty of Sheffeld Sheffeld, Unted Kngdom Copyrght 06 Asmala Ahmad and Shaun uegan. Ths artcle s dstrbuted under the Create Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, proded the orgnal work s properly cted. Abstract A practcal concept of assessng the qualty of restored data based on sgnal to nose rato SNR s reported. The data come from remote sensng satellte and has undergone restoraton process due to atmospherc haze effects. The restoraton noles remong haze mean due to haze scatterng and haze randomness due to haze spatal arablty. The results shows that the SNR of restored data can be computed f the haze mean and haze randomness components are known. Keywords: aze, Remote Sensng, Sgnal to Nose rato Introducton Atmospherc haze causes sblty to drop, therefore affectng data acqured usng optcal sensors on board remote sensng satelltes [7], [0], []. aze modfes the spectral and statstcal propertes of remote sensng data so causng problems to data users [4], [5], [6]. Ths ssue s partcularly true for optcal system such as Landsat USA, SPOT France and RazakSAT Malaysa [], [], [3].

2 444 Asmala Ahmad and Shaun uegan Degradaton of satellte data s caused by two key components, haze scatterng and sgnal attenuaton [0], whch can be represented by a statstcal model. In [8], the statstcal model for hazy satellte data can be expressed as: L V β V T L β V O where L V, T,, Lo, β and β are the hazy dataset, the sgnal component, the pure haze component, the radance scattered by the atmosphere, the sgnal attenuaton factor and the haze weghtng n satellte band, respectely. can be expressed as: Where s the haze mean, whch s assumed to be unform wthn the mage or sub-regon of the mage, and s a zero-mean random arable correspondng to haze randomness. ence: Var Var 3 So Equaton can be wrtten as: L V β V T LO β V 4 In order to remoe the haze effects [4], [5], we need to remoe both the weghted haze mean β V and the aryng component β V and deal wth the sgnal attenuaton factor β V. From [8], the effects of β V to data qualty are not sgnfcant, so we wll not consder ther remoal throughout the analyss. We normally do not hae pror knowledge about β V therefore we need to estmate t from the hazy data tself. If the estmate s β V, subtractng t from L V yelds: L V L Z V β V β V T LO β V β V 5 Equaton 5 becomes: L V β Z V T β V β V β V L O 6

3 ualty assessment of restored satellte data 445 where β V β V s the error assocated wth the dfference between the deal and estmated weghted haze mean. A common way to measure the accuracy of restored data s to compare ts qualty wth uncorrupted data [], [3], [4]. Vsual analyss offers a fast and smple way to do ths, but suffers from possble analyst bas. ence we propose two quanttate approaches to assess the qualty of restored data. Sgnal to Nose Rato One measure of performance for sngle band data s the sgnal-to-nose rato SNR, whch quantfes how seerely data hae been degraded by nose [9]. SNR s defned as the rato between the squared rato of sgnal ampltude and nose ampltude: SNR A S A N where PS and AS are sgnal power and ampltude respectely, and smlarly for nose. SNR also can be measured on a decbel scale db: P S AS SNR db 0log 0 SNR 0log0 0log0 8 PN A N The expresson for SNR and ts estmates ary between: a orgnal hazy data wth nonzero-mean nose, b hazy data after subtractng the haze mean and c restored data after flterng. From Equaton, the SNR of hazy data wth nonzero-mean haze nose can be expressed as: 7 SNR { β V T L O β V O O β V T β V T L L β V O O β V T L β V T L β V 9 O O β V T L β V T L β V Var

4 446 Asmala Ahmad and Shaun uegan snce by assumpton β V and β V are the same for all pxels n the scene. Note that here we assume β V T from the hazy data to be the sgnal ampltude because the effects of β V to data qualty s neglgble; ths apples for all cases. Due to the dscrete propertes of the hazy data, the exact alues are replaced by ther estmates: { β V T L O m n m n m n β V 0 where m and n are the numbers of pxels n the rows and columns of the mage respectely. Note that such calculaton s only possble f the alues of T,,, β V, β V, m and n are known apror e.g. smulated dataset. The exact SNR of degraded data after subtracton of the weghted haze mean can be expressed as: SNR { β V T L O { β V β V β V and can be estmated by: m n { β V T L O m n { β V β V β V Subsequently, the degraded data undergo spatal flterng. From Equaton 5.9, for lnear flterng, the exact SNR of restored data can be expressed as:

5 ualty assessment of restored satellte data 447 SNR { β V T L O ˆf V β V T L { β V T L O β V h lnear T h lnear β V β V β V hlnear L O β V T L O O { β V T L O β V hlnear T T h lnear β V β V β V hlnear 3 and can be estmated by: m n m n { β V T L O m n β V hlnear T T h β V β V β V h lnear lnear 4 For medan flterng, the exact SNR can be expressed as: SNR { β V T L O ˆf V β V T { β V T L O β V T β V β V Medan β V L O β V T L O 5

6 448 Asmala Ahmad and Shaun uegan and ts estmate by: m n m n { β V T L O m n β V T β V β V Medan β V L O β V T L O 6 3 The SNR of Restored Data when the aze Mean s Known Exactly When the haze mean s known exactly, β V β V 0 and therefore can be elmnated. ence the SNR after subtracton of the haze mean s: { β V T L O m n m n m n β V For lnear flterng we hae: 7 { β V T L O m n { β V hlnear T T β V hlnear m n 8 For medan flterng we hae: m n n { β V T L O O m n Medan β V T β V L β V T L O 9

7 ualty assessment of restored satellte data Concluson In ths paper, we hae proposed a general concept of assessng the qualty of restored data based on SNR. The SNR of restored data depends ery much on the a pror knowledge of the haze mean and haze randomness components. These components ncrease as sblty decreases and therefore need to be known n order to remoe haze and fnally to estmate the SNR of restored data. Acknowledgements. We would lke to thank Unerst Teknkal Malaysa Melaka for fundng ths study under FRGS Grant FRGS//04/ICT0/FTMK/ 0/F0045 and Agency Remote Sensng Malaysa for prodng the data. References [] A. Ahmad, Classfcaton Smulaton of RazakSAT Satellte, Proceda Engneerng, 53 03, [] A. Ahmad and S. uegan, Analyss of maxmum lkelhood classfcaton technque on Landsat 5 TM satellte data of tropcal land coers, Proceedngs of 0 IEEE Internatonal Conference on Control System, Computng and Engneerng ICCSCE0, 0, [3] A. Ahmad and S. uegan, Comparate analyss of supersed and unsupersed classfcaton on multspectral data, Appled Mathematcal Scences, 7 03, no. 74, [4] A. Ahmad and Mohd Khanap Abdul Ghan, aze reducton n remotely sensed data, Appled Mathematcal Scences, 8 04, no. 36, [5] A. Ahmad and S. uegan, The Effects of haze on the spectral and statstcal propertes of land coer classfcaton, Appled Mathematcal Scences, 8 04, no. 80, [6] A. Ahmad and S. uegan, The effects of haze on the accuracy of satellte land coer classfcaton, Appled Mathematcal Scences, 9 05, no. 49,

8 450 Asmala Ahmad and Shaun uegan [7] A. Asmala, M. ashm, M. N. ashm, M. N. Ayof and A. S. Bud, The use of remote sensng and GIS to estmate Ar ualty Index AI Oer Pennsular Malaysa, GIS Deelopment, 006, 5. [8] A. Ahmad and S. uegan, aze modellng and smulaton n remote sensng satellte data, Appled Mathematcal Scences, 8 04, no. 59, [9] J. R. Jensen, Introductory Dgtal Image Processng: A Remote Sensng Perspecte, Pearson Prentce all, New Jersey, USA, 996. [0] M. F. Razal, A. Ahmad, O. Mohd and. Sakdn, uantfyng haze from satellte usng haze optmzed transformaton OT, Appled Mathematcal Scences, 9 05, no. 9, [] M. ashm, K. D. Kannah, A. Ahmad, A. W. Rasb, Remote sensng of tropospherc pollutants orgnatng from 997 forest fre n Southeast Asa, Asan Journal of Geonformatcs, 4 004, [] M. Story and R. Congalton, Accuracy assessment: a user's perspecte, Photogrammetrc Engneerng and Remote Sensng, 5 986, [3] U. K. M. ashm and A. Ahmad, The effects of tranng set sze on the accuracy of maxmum lkelhood, neural network and support ector machne classfcaton, Scence Internatonal-Lahore, 6 04, no. 4, [4] J. R. Thomlnson, P. V. Bolstad, and W. B. Cohen, Coordnatng methodologes for scalng landcoer classfcatons from ste-specfc to global: steps toward aldatng global map products, Remote Sensng of Enronment, , Receed: Aprl 8, 06; Publshed: July 8, 06