Final Project for ECE 533 Zhenglong Li 1Automatic processing to restore data of MODIS band 6 --Final Project for ECE 533 Zhenglong Li Abstract An automatic processing to restore data of MODIS band 6 is introduced. For each granule of MODIS data, 60% of the good data in band 6 can be used for linear regression. Then the other 40% bad data can be corrected using the linear regression coefficients. After this, the Wiener filter is used to find the optimal estimation of the original image. Then the 3×3 median filter is used to remove some noise pixels. This method is compared with median, notch, and Gaussian filters. Introduction The Moderate Resolution Imaging Spectroradiometer (MODIS) is one of five instruments aboard the Terra Earth Observing System (EOS) platform launched in December 1999. After achieving final orbit, MODIS began earth observations in late February 2000 and has been acquiring data since that time. The instrument is also being flown on the Aqua spacecraft, launched in May 2002. Terra MODIS and Aqua MODIS are viewing the entire Earth's surface every 1 to 2 days, acquiring data in 36 spectral bands. These data improve our understanding of global dynamics and processes occurring on the land, in the oceans, and in the lower atmosphere. MODIS is playing a vital role in the development of validated, global, interactive Earth system models, which are able to predict global change accurately enough to assist policy makers in making sound decisions concerning the protection of our environment. However, some MODIS bands on Terra do not work well. Fig 1 (left) is an image of a granule of Terra/MODIS band 6. The value in the figure is the reflectance. According to physics, the value should be between 0 and 1. This is an image of Hurricane Isabel on September 17, 2003. As we can see, the quality of the data in band 6 is very low. A large number of the pixels are degraded, which makes the data useless at all. Actually, the percentage of the bad pixels to all the pixels is as high as 40%. Fig. 2 is zoomed part of the rectangled part in fig. 1. It‘s the first 64×64 pixels in fig. 1. In this figure, it is clear that the maximum number of rows of consecutive good data is only 3. Also, it can be found the degradation is periodical ( one example of the period is labeled).If we use “1” to represent 1 row of successful scanning, “0” to represent 1 row of bad scanning, then during one period, the sequence of the scanning is 1011011100 from up to down.Final Project for ECE 533 Zhenglong Li 2Here, we can also see the percentage of bad data is 40%, which means there are 60% of the total data are good. Currently, researchers don’t use this band because of its low quality. However, this band is very important. It has been widely used for detection of snow/cloud/aerosol. Much work has been done based on Aqua/MODIS band 6. Therefore, in my project, I will try to use the tool of image restoration to re-construct data of band 6, especially for the bad data, which appear white lines in Fig 1. Fig. 1 Image of Terra/MODIS band 6 (left) and band 7 (right). Approach First, we will treat the degradation is caused by noise alone. We will use spatial and frequency domain filtering to try to remove the noise. For the spatial domain filtering, median filters are used. For frequency domain filtering, a periodic noise filter (notch filter) and Gaussian low-pass filter are used. 3×3 median filter (spatial domain filter) As its name indicates, the median filter replaces the value of a pixel by the median of the gray levels in the 3×3 neighborhood. )},({),(33),(tsgyxfmediants ×∈= If this filter doesn’t work, then a 7×7 median filter will be used in order to achieve better results. Notch filter (frequency domain filter) There are two reasons why this filter is used. One is that the noise is periodic, as shown in theFinal Project for ECE 533 Zhenglong Li 3introduction section. The other reason is that the pattern in frequency domain in our case has some strange features, which might be features of periodic noise. Fig. 3 (left) is the Fourier transform of Fig. 1. There are at least two strange features, which are caused by the noise. One is that two bright lines along x-coordinate and y-coordinate. Generally, the bright part only relies in the center of the image after Fourier transfer. The other strange feature is that there are four pairs of bright areas along the y-coordinate. As shown in the textbook, the Fourier transform of a pure sine is a pair of impulses. This might be able to remove the noise. Fig. 2 Zoomed part of fig. 1 (an example of one period is shown) The notch filter here includes two parts. One is used to remove the two bright lines, the other one is used to remove the four pairs of bright areas. Since the two lines are along the x and y coordinates, the filter dealing with this is ===otherwiseNvorMuifvuH12/2/0),( Where M is the width of the image, N is the height of the image. The four pairs of the bright areas are along the y coordinate. The filter dealing with them is ≤≤=otherwiseDvuDorDvuDifvuH1),(),(0),(0201 where ()( )[]2/120212/2/),( vNvMuvuD −−+−= ()( )[]2/120222/2/),( vNvMuvuD +−+−=Final Project for ECE 533 Zhenglong Li 4And the center of one pair of bright areas are )2/,2/(0vNM+ and )2/,2/(0vNM − . In this way, the frequencies contained in the notch areas (the two lines and the bright areas) are removed. Fig. 3 Fourier transfer of the original image and the reconstructed original image Reconstruction of imagery original image using other band In reality, band 7 is used instead of band 6 when band 6 is bad because the radiative transfer properties of the two bands are very similar. Thus these two bands must have some similarity. Fig. 1 (right) is the image of band 7. From this good-quality image, the structure of the hurricane is very clear and it is almost same as band 6. In order to retrieve the relationship between band 6 and band 7, some of the data are taken to plot the scattering fig. 4. Clearly, there is a linear relation between band 6 and band 7. Also, the bad data (the line of x=2.3) are well separated in this way. It is bad data because reflectance can’t be larger than 1. Let y=band 6 (except the bad data), x is the corresponding band 7. Construct the linear model as εββ++= xy10 Use least square to do linear regression to
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