CBERS simulation from SPOT and its restoration Gerald Jean Francis Banon and Leila Maria Garcia Fonseca Content 1 CBERS Band 4 simulation from SPOT 1.1 Along line MTF of CBERS Band 4 1.2 Along line MTF of SPOT Band 3 1.3 Along line MTF of the simulation filter 1.4 Along line simulation filter kernel 1.5 MTF of the file effect 1.6 Along track MTF of CBERS Band 4 1.7 Along track MTF of SPOT Band 3 1.8 Along track MTF of the simulation filter 1.9 Along track simulation filter kernel 1.10 Simulation filter kernel 2 CBERS Band 4 Restoration 2.1 Along line MTF of the restoration filter 2.2 Along line restoration filter kernel 2.3 Along track MTF of the restoration filter 2.4 Along track restoration filter kernel 2.5 Restoration filter kernel 3 CBERS Band 4 Restoration within a window 3.1 Along line MTF of the attenuation filter 3.2 Along line MTF of the restoration filter 3.3 Along line restoration filter kernel 3.4 Along track MTF of the attenuation filter 3.5 Along track MTF of the restoration filter 3.6 Along track restoration filter kernel 3.7 Restoration filter kernel 1 CBERS simulation from SPOT 1.1 Along line MTF of CBERS Band 4 function c=cbers1 f(1)=1; f(2)=1; f(3)=.98; f(4)=.88; f(5)=.70; f(6)=.56; f(7)=.42; f(8)=.32; f(9)=.28; f(10)=.22; f(11)=.18; f(12)=.15; f(13)=.12; f(14)=.11; f(15)=.085; f(16)=.08; f(17)=.075; f(18)=.07; f(19)=.065; f(20)=.06; for i=1:19 c(i+1)=f(i+1); c(i+20)=f(21-i); end c(1)=f(1); figure x=cbers1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 1 - Along line MTF of CBERS Band 4') see plot 1.2 Along line MTF of SPOT Band 3 The MTF is gaussian with parameter sigma = 11,2906 m (Begni & Rayssiguiar, 1983) 1/(2*19.5) 1/meter <--> 38.5 lp/mm x 1/meter <--> 38 lp/mm 38 lp/mm is chosen as half the sample frequency for the sake of simplicity when computing later the Point Spread Function (PSF). x=(38/38.5)/(2*19.5) function s=spot1 N=19; f(1)=1; for n=1:19 u=(n/N)*(38/38.5)/(2*19.5); f(n+1)=exp(-2*(3.1416^2)*(11.2906^2)*(u^2)); end for i=1:19 s(i+1)=f(i+1); s(i+20)=f(21-i); end s(1)=f(1); x=spot1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 2 - Along line MTF of SPOT Band 3') see plot 1.3 Along line MTF of the simulation filter function f=filter1 c=cbers1; s=spot1; for i=1:39 f(i)=c(i)/s(i); end x=filter1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 3 - Along line MTF of the simulation filter') see plot 1.4 Along line simulation filter kernel x=real(fft(filter1,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 4 - Along line PSF for the CBERS simulation') see plot function k=kernel1 x=real(fft(filter1,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernel1 0.0216 0.0944 0.1646 0.4391 0.1646 0.0944 0.0216 1.5 MTF of the file effect function s=file N=19; f(1)=1; for n=1:19 u=(n/N)*(38/38.5)/(2*19.5); f(n+1)=sin(3.1416*u*19.5)/(3.1416*u*19.5); end for i=1:19 s(i+1)=f(i+1); s(i+20)=f(21-i); end s(1)=f(1); x=file; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 5 - MTF of the file effect') see plot 1.6 Along track MTF of CBERS Band 4 function f=cbers2 b=file; c=cbers1; for i=1:39 f(i)=b(i)*c(i); end x=cbers2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 6 - Along track MTF of CBERS Band 4') see plot 1.7 Along track MTF of SPOT Band 3 The MTF is gaussian with parameter sigma = 10,3840 m (Begni & Rayssiguiar, 1983) function s=spot2 N=19; f(1)=1; for n=1:19 u=(n/N)*(38/38.5)/(2*19.5); f(n+1)=exp(-2*(3.1416^2)*(10.3840^2)*(u^2)); end for i=1:19 s(i+1)=f(i+1); s(i+20)=f(21-i); end s(1)=f(1); x=spot2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 7 - Along track MTF of SPOT Band 3') see plot 1.8 Along track MTF of the simulation filter function f=filter2 b=file; c=cbers1; s=spot2; for i=1:39 f(i)=b(i)*c(i)/s(i); end x=filter2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 8 - Along track MTF of the simulation filter') see plot 1.9 Along track simulation filter kernel x=real(fft(filter2,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 9 - Along track PSF for the CBERS simulation') see plot function k=kernel2 x=real(fft(filter2,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernel2 0.0292 0.0885 0.1889 0.3868 0.1889 0.0885 0.0292 1.10 Simulation filter kernel kernel2'*kernel1 0.0006 0.0028 0.0048 0.0128 0.0048 0.0028 0.0006 0.0019 0.0084 0.0146 0.0389 0.0146 0.0084 0.0019 0.0041 0.0178 0.0311 0.0829 0.0311 0.0178 0.0041 0.0083 0.0365 0.0637 0.1699 0.0637 0.0365 0.0083 0.0041 0.0178 0.0311 0.0829 0.0311 0.0178 0.0041 0.0019 0.0084 0.0146 0.0389 0.0146 0.0084 0.0019 0.0006 0.0028 0.0048 0.0128 0.0048 0.0028 0.0006 2 CBERS Band 4 Restoration 2.1 Along line MTF of the restoration filter In this secftion, the restoration objective is to return to the SPOT Band 3 along line MTF function r=restoration1 c=cbers1; s=spot1; for i=1:39 r(i)=s(i)/c(i); end x=restoration1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 10 - Along line MTF of the restoration filter') see plot 2.2 Along line restoration filter kernel x=real(fft(restoration1,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 11 - Along line PSF for the CBERS restoration') see plot function k=kernelForRestoration1 x=real(fft(restoration1,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernelForRestoration1 0.1907 -0.3224 -0.8181 2.8997 -0.8181 -0.3224 0.1907 2.3 Along track MTF of the restoration filter In this section, the restoration objective is to return to the SPOT Band 3 along track MTF function r=restoration2 c=cbers2; s=spot2; for i=1:39 r(i)=s(i)/c(i); end x=restoration2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 12 - Along track MTF of the restoration filter') see plot 2.4 Along track restoration filter kernel x=real(fft(restoration2,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 13 - Along track PSF for the CBERS restoration') see plot function k=kernelForRestoration2 x=real(fft(restoration2,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernelForRestoration2 0.1694 -0.0908 -1.5746 3.9920 -1.5746 -0.0908 0.1694 2.5 Restoration filter kernel kernelForRestoration2'*kernelForRestoration1 0.0323 -0.0546 -0.1386 0.4912 -0.1386 -0.0546 0.0323 -0.0173 0.0293 0.0743 -0.2633 0.0743 0.0293 -0.0173 -0.3002 0.5076 1.2882 -4.5660 1.2882 0.5076 -0.3002 0.7611 -1.2870 -3.2660 11.5758 -3.2660 -1.2870 0.7611 -0.3002 0.5076 1.2882 -4.5660 1.2882 0.5076 -0.3002 -0.0173 0.0293 0.0743 -0.2633 0.0743 0.0293 -0.0173 0.0323 -0.0546 -0.1386 0.4912 -0.1386 -0.0546 0.0323 3 CBERS Band 4 Restoration within a window 3.1 Along line MTF of the attenuation filter Following Fonseca (1988, p. 97). 1/(2*19.5) 1/meter <--> 38.5 lp/mm x 1/meter <--> 11 lp/mm 11 lp/mm is chosen as the frequency at 0.5 of the along line CBERS MTF. x=(11/38.5)/(2*19.5) function w=window1 N=19; f(1)=1; uw=(11/38.5)/(2*19.5); uc=1/(2*19.5); for n=1:19 u=(n/N)*(38/38.5)/(2*19.5); if (u<=uw) f(n+1)=1; else f(n+1)=0.5*(1+cos(3.1416*(u-uw)/(uc-uw))); end end for i=1:19 w(i+1)=f(i+1); w(i+20)=f(21-i); end w(1)=f(1); x=window1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 14 - Along line MTF of the attenuation filter') see plot 3.2 Along line MTF of the restoration filter function r=restorationb1 c=cbers1; s=spot1; w=window1; for i=1:39 r(i)=s(i)*w(i)/c(i); end x=restorationb1; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 15 - Along line MTF of the restoration filter') see plot 3.3 Along line restoration filter kernel x=real(fft(restorationb1,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 16 - Along line PSF for the CBERS restoration') see plot function k=kernelForRestorationb1 x=real(fft(restorationb1,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernelForRestorationb1 0.0536 -0.6970 0.2413 1.8043 0.2413 -0.6970 0.0536 3.4 Along track MTF of the attenuation filter Following Fonseca (1988, p. 97). 1/(2*19.5) 1/meter <--> 38.5 lp/mm x 1/meter <--> 11 lp/mm 11 lp/mm is chosen as the frequency at 0.5 of the along track CBERS MTF. x=(11/38.5)/(2*19.5) function w=window2 N=19; f(1)=1; uw=(11/38.5)/(2*19.5); uc=1/(2*19.5); for n=1:19 u=(n/N)*(38/38.5)/(2*19.5); if (u<=uw) f(n+1)=1; else f(n+1)=0.5*(1+cos(3.1416*(u-uw)/(uc-uw))); end end for i=1:19 w(i+1)=f(i+1); w(i+20)=f(21-i); end w(1)=f(1); x=window2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 17 - Along track MTF of the attenuation filter') see plot 3.5 Along track MTF of the restoration filter function r=restorationb2 c=cbers2; s=spot2; w=window2; for i=1:39 r(i)=s(i)*w(i)/c(i); end x=restorationb2; plot(0:2:38,x(1:20)) xlabel('lp/mm') title('Figure 18 - Along track MTF of the restoration filter') see plot 3.6 Along track restoration filter kernel x=real(fft(restorationb2,39)); plot(0:19,x(1:20)) xlabel('pixel') title('Figure 19 - Along track PSF for the CBERS restoration') see plot function k=kernelForRestorationb2 x=real(fft(restorationb2,39)); k(1)=x(4); k(2)=x(3); k(3)=x(2); k(4)=x(1); k(5)=x(2); k(6)=x(3); k(7)=x(4); a=0; for i=1:7 a=a+k(i); end for i=1:7 k(i)=k(i)/a; end kernelForRestorationb2 0.1569 -0.8236 0.1326 2.0680 0.1326 -0.8236 0.1569 3.7 Restoration filter kernel kernelForRestorationb2'*kernelForRestorationb1 0.0084 -0.1094 0.0379 0.2832 0.0379 -0.1094 0.0084 -0.0441 0.5740 -0.1987 -1.4860 -0.1987 0.5740 -0.0441 0.0071 -0.0924 0.0320 0.2393 0.0320 -0.0924 0.0071 0.1108 -1.4415 0.4990 3.7315 0.4990 -1.4415 0.1108 0.0071 -0.0924 0.0320 0.2393 0.0320 -0.0924 0.0071 -0.0441 0.5740 -0.1987 -1.4860 -0.1987 0.5740 -0.0441 0.0084 -0.1094 0.0379 0.2832 0.0379 -0.1094 0.0084 Bibliography @Article{Banon:1990:SIB, author = "Banon, G", title = "simulacao de imagens de baixa resolucao", journal = "Controle & Automacao", year = "1990", volume = "2", number = "3", pages = "180-192", month = "March", note = "INPE-8900-PRE/899", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "Banon:1990:SIB", entrytype = "Article", type = "PRE", } @TechReport{BanonSant:1993:DFD, author = "Banon, Gerald Jean Francis and Santos, Ailton Cruz dos", title = "Digital filter design for sensor simulation application to the Brazilian Remote Sensing Satellite", institution = "INPE", year = "1993", type = "RPQ", address = "Sao Jose dos campos", note = "INPE-5523-RPQ/665", abstract = "Neste artigo, um modelo de interacao, entre um sensor de baixa resolucao com largo campo de visada a bordo de um satelite de observacao da terra, e a superficie da terra e apresentado. O sensor simulado e obtido atraves da composicao de um algoritmo de simulacao digital por um sensor de alta resolucao e menor campo de visada. Uma nova tecnica de desenvolvimento de filtro digital e proposto para aproximar um filtro Gaussiano ideal. O filtro resultante pode ser implementado em qualquer plataforma existente de processamento de imagens. Finalmente, dois retahos de imagem, da maneira que eles seriam produzidos pelo SSR (Satelite de Sensoriamento Remoto) da MECB (Missao Espacial Completa Brasileira) a partir de uma cena LANDSAT-TM (Thematic Mapper) sao apresentadas como exemplo..", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "BanonSant:1993:DFD", entrytype = "TechReport", } @MastersThesis{Fonseca:1988:RII, author = "Fonseca, Leila Maria Garcia", title = "Restauracao e interpolacao de imagens do satelite Landsat por meio de tecnicas de projeto de filtros FIR", school = "ITA", year = "1988", address = "Sao Jose dos Campos", month = "April", note = "INPE-8898-TAE/898", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "Fonseca:1988:RII", entrytype = "MastersThesis", program = "DPI", type = "TAE", } @InProceedings{FonsecaBano::DTF, author = "Fonseca, Leila Maria Garcia and Banon, Gerald Jean Francis", title = "Duas tecnicas de filtragem espacial para simular a resolucao espacial ao Nadir do satelite de sensoriamento remoto brasileiro", booktitle = "Simposio Brasileiro de Computacao Grafica e Processamento de Imagens, 2", pages = "69-76", month = "April", note = "INPE-8023-PRE/023", abstract = "Este trabalho apresenta duas tecnicas de filtragem espacial para simular a resolucao espacial ao nadir do Satelite de Sensoriamento Remoto brasileiro (SSR). Estas duas tecnicas sao avaliadas atraves da sua aplicacao na simulacao de imagens MSS. Posteriormente, os filtros sao aplicados para simular a banda 1 so SSR a partir da banda 3 do TM. De um modo geral, os resultados mostraram-se satisfatorios.", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "FonsecaBano::DTF", entrytype = "InProceedings", type = "PRE", } @InProceedings{FonsecaMascBano:1987:TRR, author = "Fonseca, Leila Maria Garcia and Mascarenhas, Nelson Delfino d'Avila and Banon, Gerald Jean Francis", title = "Tecnicas de restauracao para remostragem de imagens do satelite Landsat-5", booktitle = "Simposio Brasileiro de Telecomunicacoes, 5", year = "1987", pages = "204-208", organization = "Sociedade Brasileira de Telecomunicaoes", month = "June", note = "INPE-4189-PRE/1076", keywords = "processamento digital e correcoes, restauracao de imagens, landsat-5, transformada de fourier, digital processing and correction, image restoration, thematic mappers (landsat)", abstract = "Sao mostrados neste trabalho alguns resultados da restauracao para reamostragem de imagens do TM (Thematic Mapper), utilizando tecnicas no dominio de Fourier. A imagem restaurada e comparada a aimagem reamostrada com o interpolador de convolucao cubica. A comparacao e feita visualmente e atraves do perfil radiometrico de uma linha da imagem.", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "FonsecaMascBano:1987:TRR", entrytype = "InProceedings", type = "PRE", } @InProceedings{MascarenhasBanoFons:1990:SPB, author = "Mascarenhas, Nelson Delfini D'Avila and Banon, Gerald Jean Francis and Fonseca, Leila Maria Garcia", title = "SPOT panchromatic band simulation by linear combination of multispectral bands", booktitle = "Simposio Brasileiro de Sensoriamento Remoto, 6", year = "1990", pages = "181-187", organization = "Instituto Nacional de Pesquisas Espaciais", note = "INPE-5295-PRE/1658", keywords = "processamento digital e correcoes, spot (satelite frances, sensores, sensors", abstract = "A simulacao de uma de mais bandas de um sensor multiespectral por combinacao de outras bandas apresenta possibilidades atraentes. Por exemplo, ela poderia diminuir a taxa de dados do canal de comunicacao entre o satelite e a terra. Neste trabalho, e feita uma analise da simulacao da banda pancromatica do SPOT (degrada espacialmente), por uma combinacao linear de bandas multiespectrais. Dois metod sao usados para a combinacao linear espectral: a) minimo quadrado sem restricao e b) minimo quadrado com restricoes de igualdade. Usando o segundo metodo mostra-se que a relacao sinal-ruido da banda simulada ttende a ser melhor que a relacao sinal-ruido de cada banda multiespectal. Os resultados experimentais incluem a simulacao espacial de uma banda pancromatica degradada espacialmente, com uma resolucao de 20 m, opara comparacao com a banda simulada espectralmente. Esses resultados demostram que uma estimativa razoavekl do ponto de vista visual e numerico da banda pancromatica degradada pode ser obtida.", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "MascarenhasBanoFons:1990:SPB", entrytype = "InProceedings", type = "PRE", } @InProceedings{MascarenhasBanoFons:1991:SAP, author = "Mascarenhas, Nelson Delfino D'Avila and Banon, Gerald Jean Francis and Fonseca, Leila Maria Garcia", title = "Simulation of a panchormatic band by spectral linear combination of multiespectral bands", booktitle = "International Symposium on Remote Sensing of Environment,24", year = "1991", organization = "ERIM", note = "INPE-5293-PRE/1698", abstract = "The simulation of one or more bands of a multispectral sensor by combination of other bands represents an attractive possibility. In this work an anlysis of the spatially degraded SPOT panchromatic band by linear combination of the multispectral bands has been performed using least squares methods. The results include 1) a theoretical study of the signal to noise ratio of the simulated band as compared with the multispectral bands, and 2) experimental work showing a numerically and visually reasonable estimate of the pancromatic band.", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "MascarenhasBanoFons:1991:SAP", entrytype = "InProceedings", type = "PRE", } @MastersThesis{Santos:1992:SIS, author = "Santos, Ailton Cruz", title = "Simulacao de Imagens de Sensores com Largo Campo de Visada a partir de Imagens de Sensores com menor Campo de Visada- O caso SSR/TM", school = "Instituto Nacional de Pesquisas Espaciais", year = "1992", address = "Sao Jose dos Campos", month = "March", note = "INPE-5378-TDI/473", keywords = "?????????, compo de visada, filtro, processamento de imagens, mapeador tematico (landsat), satelites landsat, computerized simulation, field of view, image enhancement, image processing, thematic mappers (landsat), adaptive filters", abstract = " Com este trabalho pretende-se a simulacao da imagem bruta obtida por um sensor orbital com largo campo de visada sob um modelo aproximado para o Satelite de Sensoriamento Remoto (SSR) da Missao Espacial completa brasileira (MECB), a partir de um conjunto de imagens obtidas por um sensor com menor campo de visada. No caso, usou-se um conjunto de imagens obtidas pelo sensor TM/Landsat, construidas com controle geometrico em uma projecao cartografica e corrigidas com pontos de controle. Utilizando-se um modelo da superficie terrestre, sao determinados os pontos na superficie correspondente a projecao do centro de cada detentor (em coordenadas geodesicas-latitude e longitude). Os valores dos pixels da imagem com largo campo de visada sao calculados a partir dos valores dos pixels da imagem TM vizinhos a estes pontos. Este calculo e feito empregando-se um filtro de simulacao adaptativo. Os resultados mostram-se satisfatorios considerando-se o aspecto geometrico sob o qual foi desenvolvido o presente trabalho.", annote = "entry from dpi.inpe.br/banon/1997/12.04.09.59", citationkey = "Santos:1992:SIS", entrytype = "MastersThesis", program = "SER", type = "TDI", }