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The accuracy of the deconvolution algorithm is evaluated by convolving a synthetic test scene, adding noise, then deconvolving the scene and analysing the differences. Initially, a standard image processing test scene (Figure 4.11(a)) is convolved with the MODIS Aqua band 8 PSF and average band 8 noise (Xiong et al., 2009) is added (Figure 4.11(b)). The difference between the original and the convolved image is displayed in Figure 4.11(c) and indicates the effect the instrument would have if the original image was rendered by MODIS Aqua band 8. This particular image contains a maximum individual pixel error of 90.01%. Figure 4.11(d) displays a frequency histogram of the pixel differences in Figure 4.11(c). The convolved image is then deconvolved using the implemented Multiscale Entropy deconvolution algorithm and the result is displayed in Figure 4.11(e). The difference between the original and the deconvolved image is displayed in Figure 4.11(f) and a frequency histogram of this difference is shown in Figure 4.11(g).

The Multiscale Entropy deconvolution algorithm removes instrument effects down to a level where no visible structures remain (Figure 4.11(f)) and the maximum individual pixel error has been reduced from 90.01% to 0.34%. The frequency histogram in Figure 4.11(g) indicates that the final pixel differences are normally distributed with a maximum magnitude of 0.18, whereas the Gaussian noise added to the original image had a maximum magnitude of 0.11. Therefore, it is clear that Multiscale Entropy deconvolution has successfully removed the instrument effects

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Figure 4.11: Synthetic data deconvolution accuracy test showing (a) the original image and (b) the original image convolved with MODIS Aqua band 8 PSF and average band 8 noise added.

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Figure 4.11 continued: Synthetic data deconvolution accuracy test showing (c) the difference between the original and convolved image and (d) a frequency histogram of (c).

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Figure 4.11 continued: Synthetic data deconvolution accuracy test showing (e) the convolved image after deconvolution with the developed algorithm and (f) the difference between the original and deconvolved image.

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Figure 4.11 continued: Synthetic data deconvolution accuracy test showing (g) a frequency histogram of (f).

from the data with a high level of accuracy.

Figure 4.12 shows an image from MODIS Aqua band 12 (546nm - 556nm) that was chosen due to the sensitivity of coastline contrast in that waveband. The original convolved and noisy data as received from MODIS Aqua is shown in Figure 4.12(a) and the deconvolved data is shown in Figure 4.12(b). Figure 4.12(c) shows the relative pixel error with an adjusted scale and represents the instrument effects that are removed from the data. These effects are further represented with a frequency histogram in Figure 4.12(d) and have a maximum individual pixel error of 19.44% for this particular image. Considerable contamination can be seen in land regions due to large changes in radiance (Figure 4.12(c)). The coastline also contains contamination with the largest errors being produced at high radiance edges. The deconvolution process has increased the brightness of the beaches and sharp edges have been resolved.

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Figure 4.12: MODIS deconvolution test showing (a) the original MODIS Aqua band 12 data (convolved and noisy) and (b) the deconvolved MODIS Aqua band 12 data. Image of Hawke Bay, New Zealand (Approx. lat/long -39.44, 177.46), 06/04/2009.

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Figure 4.12 continued: MODIS deconvolution test showing (c) the rescaled relative error removed from the original data and (d) a frequency histogram of the relative error. Image of Hawke Bay, New Zealand (Approx. lat/long -39.44, 177.46), 06/04/2009.

Figure 4.13 shows the deconvolution of an open-ocean scene from MODIS Aqua band 12. This scene has undergone the same process as the previous example but highlights an extreme case where bright clouds contaminate dark ocean measurements. Figures 4.13(a) and 4.13(b) show the convolved and deconvolved MODIS Aqua band 12 images. The rescaled relative pixel error is displayed in Figure 4.13(c) and its frequency histogram is shown in Figure 4.13(d). The maximum individual pixel error for this scene reaches 114.63% which is significantly larger than the previous coastal scene example (Figure 4.12). The largest contamination errors are observed immediately around high-contrast cloud edges. However, the large spatial extent of the PSF causes water regions close to clouds, within approximately 20km, to experience moderate instrumental distortion. This contamination becomes even more severe for pockets of water that are surrounded by cloud cover. In this case, Multiscale Entropy deconvolution successfully removes instrumental distortion and restores accurate ocean measurements in high-contrast areas.

In removing the radiance contamination caused by the instrument optics, a greater quantity of ocean measurements become available for processing. Without deconvolution, ocean measurements near cloud edges are flagged for removal and do not contribute to the final data products. This reduces the spatial coverage and availability of ocean measurements and can detrimentally impact the usefulness of satellite imagery. When the instrumental distortion is removed via Multiscale Entropy deconvolution, a significant number of valuable ocean measurements are recovered and can then contribute to downstream satellite data products, which improves the spatial coverage and availability of the data.

The bow-tie effect of scanning-based satellite instruments has the potential to introduce inaccuracies into the deconvolution process. As a result of bow-tie effects, the number of spatially duplicate measurements increases towards the left and right edges of a MODIS scene. This effect is most extreme at these edges and is present in level 1A MODIS data on which the deconvolution algorithm operates. The deconvolution process can introduce radiometric inaccuracies into these areas where spatial contrast is observed due to the contribution of duplicate measurements. This effect does not occur for deconvolution at the centre of a MODIS scene where there

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Figure 4.13: MODIS deconvolution test showing (a) the original MODIS Aqua band 12 data (convolved and noisy) and (b) the deconvolved MODIS Aqua band 12 data. Image of Southern Pacific Ocean (Approx. lat/long -45, 150), 21/04/2010.

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Figure 4.13 continued: MODIS deconvolution test showing (c) the rescaled relative error removed from the original data and (d) a frequency histogram of the relative error. Image of Southern Pacific Ocean (Approx. lat/long -45, 150), 21/04/2010.

are no duplicate measurements. A possible solution to this problem could employ a mask-based method to account for measurement duplication and prevent errors from being introduced during deconvolution. However, this process has not been included in the developed implementation. Wherever possible, the measurements analysed in this thesis have been taken from regions away from the edge of MODIS scene.