福爾摩沙衛星五號(福衛五號，FS-5)搭載的光學遙測儀(Remote Sensing Instrument, RSI)具有2公尺全色態與4公尺多光譜的高空間解析度，而高解析度光學衛星為確保品質在升空前後都必須進行輻射校正，包含絕對與相對校正，其中相對輻射校正主要為移除感測元件間光譜反應之差異，此差異大多反應於影像中的條紋現象。用濾波法進行相對輻射校正的方法有許多，但傳統之傅立葉轉換與小波轉換都須要做基底的假設，而近代發展的經驗模態分解法(Empirical Mode Decomposition, EMD)並未考慮雜訊的影響，造成相對校正結果之誤差，所以本研究嘗試使用將雜訊納入考量的改良式濾波法—系集經驗模態分解法(Ensemble Empirical Mode Decomposition, EEMD)，針對福衛五號升空前、後之觀測影像進行相對輻射校正之測試，藉此獲取感測器元件之最佳等化係數以校正感測元件間光譜反應之差異，期能提供福衛五號遙測儀器(FS-5 RSI)相對輻射校正作業化流程之參考。
研究結果顯示，以增益值1為例，EEDM在升空前、後影像相對校正結果的標準差(分別為全色態: 4.85，綠光: 1.56，藍光: 1.81，近紅外: 1.52和全色態: 6.42，紅光: 4.35，藍光: 5.24，近紅外: 5.19)較EDM的結果(分別為全色態: 6.39，綠光: 2.93，藍光: 2.98，近紅外: 2.90和全色態: 9.52，紅光: 6.76，藍光: 8.06，近紅外: 9.59)為佳，其改善之百分比可高達90%以上。此一結果亦說明雜訊之考量在率定FS-5 RSI等化係數之重要性，尤其是升空前、後RSI因環境差所造成雜訊的變化，亦將明顯地影響等化係數之校正。更重要的是，FS-5 RSI升空後之雜訊亦將隨時間而有所變化，因此本研究(EEDM)所考量雜訊之影響確實可以滿足實際觀測影像之需求，對於福衛五號遙測儀器(FS-5 RSI)相對輻射校正作業化具有相當的實用性與參考價值。

Remote Sensing Instrument (RSI) is the primary optical sensor on board FORMOSAT-5 (FS-5), which can provide 2-meter in panchromatic and 4-meter in multi-spectral of high-spatial-resolution imagery. To maintain the radiometric quality, the periodical radiometric calibration is essential no matter before and after launched. For the relative radiometric calibration which related to the non-uniform response between detectors, the general methods for relative radiometric calibration such as Fourier transform and wavelet transform, are usually under the assumption of presetting basic functions without considering the noise. Although the modern development method named Empirical Mode Decomposition(EMD) is suitable for the relative calibration of non-stable signal but still been affected by the noise. Therefore, this study focuses on the issue caused from noise for improving the result of relative calibration. The Ensemble Empirical Mode Decomposition(EEMD) method is applied to calibrate FS-5 pre-flight and on-orbit data for relative radiometric calibration of RSI by considering the effect of noise.
The calibration results show that all the calibrated results of EEMD are better than EMD results for both pre-flight and on-orbit images. Taking the results of gain number 1 (G1) for example, standard deviation of calibrated imageries using EEMD (pre-flight: PAN: 4.85, B2: 1.56, B3: 1.81, B4: 1.52, on-orbit: PAN: 6.42, B1: 4.35, B3: 5.24, B4: 5.19) is lower than EMD (pre-flight: PAN:6.39, B2: 2.93, B3: 2.98, B4: 2.90, on-orbit: PAN: 9.52, B1: 6.76, B3: 8.06, B4: 9.59) and the improving ratio can up to 90%. The results also indicate that the impact of noise is significant to FS-5 RSI relative response coefficients. More importantly, the proposed EEMD approach can further facilitate the operational procedure of FS-5 RSI relative calibration under the conditions which the noise changes as time goes by.

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