Automatic processing to restore data of MODIS band 6

Transcription

1 Automatic processing to restore data of MODIS band 6 --Final Project for ECE 533 Abstract An automatic processing to restore data of MODIS band 6 is introduced. For each granule of MODIS data, 6% of the good data in band 6 can be used for linear regression. Then the other 4% 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 After achieving final orbit, MODIS began earth observations in late February and has been acquiring data since that time. The instrument is also being flown on the Aqua spacecraft, launched in May. Terra MODIS and Aqua MODIS are viewing the entire Earth's surface every 1 to 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 and 1. This is an image of Hurricane Isabel on September 17, 3. 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 4%. Fig. is zoomed part of the rectangled part in fig. 1. It s the first 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, to represent 1 row of bad scanning, then during one period, the sequence of the scanning is from up to down. 1

2 Here, we can also see the percentage of bad data is 4%, which means there are 6% 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. Approach Fig. 1 Image of Terra/MODIS band 6 (left) and band 7 (right). 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. f ( x, y) = { g( s, t)} median ( s, t) 3 3 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 the

3 introduction 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. 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 if u = M / or v = N / H ( u, = 1 otherwise 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 H ( u, = 1 if D ( u, D 1 otherwise or D ( u, D where [( u M / ) + ( v N / ) ] 1/ [( u M / ) + ( v N / ) ] 1/ D ( v 1 u, = D ( + v u, = 3

4 And the center of one pair of bright areas are M /, N / + v ) and M /, N / v ). 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=.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 y 1 = β + β x + ε Use least square to do linear regression to obtain the coefficients. Then use the coefficients to predict the value of band 6. Thus, an imagery original image of band 6 is obtained. Wiener filter With the imagery original image, the degradation function can be estimated. Let f be the imagery original image, g be the degraded image, and F and G be their corresponding Fourier 4

5 transforms. Then the degradation function can be estimated by G( u, H ( u, = F( u, According to Wiener filter, ˆ Huv (, ) Guv (, ) (, ) = Huv (, ) + S( uv, )/ S(, ) H ( uv, ) η f uv Fuv where H(u, is the degradation function G(u, is the Fourier transform of the degraded image S η (u, is the power spectrum of the noise S f (u, is the power spectrum of the undegraded image Fig. 4 Scattering between band 6 ( x-coordinate) and band 7 ( y-coordinate) For satellite remote sensing, the signal-to-noise ratio (SNR) is given. For example, the SNR for band 6 and band 7 of MODIS is 75 and 11 respectively. Thus, the ratio between S η (u, and S f (u, is a constant. Thus ˆ Huv (, ) Guv (, ) (, ) = H ( uv, ) Fuv Huv (, ) + K where K = 1/75. With F ( u,, the estimated original image f ( x, y) can be obtained through inverse Fourier transform. After this, additional conventional noise examination algorithm (median filter, Gaussian 5

6 low-pass filter) will be conducted to make better quality. Fig. 5 The reconstructed imagery original image (left) and the reconstructed original image using Wiener filter (right) Results During this section, the reconstructed imagery original image and the reconstructed original image are show first. Then we will focus on the comparison of the results after various filters (median, notch and Gaussian filters). The comparison is between results before and after the reconstruction of the original image. Fig. 6 Difference between the reconstructed imagery original image and the reconstructed original image using Wiener filter Fig. 5 shows the reconstructed images. The left is the reconstructed imagery original image 6

7 (using linear regression, the correlation coefficient is.9538) and the right is the reconstructed original image (using Wiener filter). It may be difficult to see the difference between the two images. Fig. 6 is the difference between the two images. The value is here is multiplied by 1. The main difference comes from low clouds, which are very bright in fig. 5. Fig. 7 Median filter for original image (left) and the reconstructed original image (right); the upper two use 3 3 median filter, the lower two are followed by 7 7 median filter Fig. 7 shows the results after median filters. The left two are for original image and the right two for the reconstructed original image. The upper two use 3 3 median filter, the lower two are followed by 7 7 median filter. After the 3 3 median filter, the two single rows of bad data are removed, while the two consecutive rows of bad data are still there. Also, the single row of good data is removed because it is between two rows of bad data. After median filtering, this line is also 7

8 bad data. Thus, we take a 7 7 median filter. The results are acceptable because the structure of the hurricane can be seen now on band 6. However, the image is blurred significantly. And many fine structures are lost. When taking the 3 3 median filter on the reconstructed original image, the blurring is not evident. And some of the noise pixels (abnormally bright) are removed. As for the 7 7 median filter, it again blurs the image significantly. Fig. 8 Notch filtering for original image (left) and the reconstructed original image (right) Reference Fig. 3 (right) shows the Fourier transform of the reconstructed image. The improvement is obvious-----the four pairs of bright areas are gone. However, the two bright lines are still there. Thus, the notch filter described in the previous section is used. Fig. 8 shows the results using notch filter. The left one is for the original image. It can not remove the noise. The strange thing here is that the image should be darker than the original one because many of its energy are removed. However, as can be seen in Fig. 4, the value of the bad data are.3, which is much larger than 1. Thus, after the notch filtering, the image is still bright. The notch filter for the reconstructed original image does not show evident improvement (now the notch filter only needs to remove the two bright lines). Fig. 9 shows the results after Gaussian low-pass filtering. The left is for the original image, and the right is for the reconstructed original image. Just like the notch filtering, the Gaussian filter can not remove the noise. And the filtered image is bright. For the reconstructed original image, the Gaussian filter tends to blur the image. Some fine structures are blurred. 8

9 Fig. 9 Gaussian low-pass filtering for original image (left) and the reconstructed original image (right) Conclusion and Discussion The processing here can be automatically conducted. For each granule of MODIS data, 6% of the good data in band 6 can be used for linear regression. Then the other 4% can be calculated 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. During the processing, the only information needed is the SNR, which is a given constant. Thus, this processing can be done automatically as soon as the new data are received on workstation. 9