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# Remote sensing images provide useful information about land cover

INSTRUCTIONS TO CANDIDATES

Question 3

Remote sensing images provide useful information about land cover. However, these images can be contaminated by clouds, shadow, or other noise. Robust principal component analysis (PCA) has obtained stunning performance in removing noise from images. It assumes such data are composed of a low-rank component and a sparse component. Mathematically, given an image matrix, M, M ∈ Rm×n, M can be decomposed into a low-rank matrix L and a sparse matrix S, which is estimated by minimizing the following constrained optimization problem:

πππ(πΏ,π)  βπΏβ∗ + π||π||1, s.t. M= L + S

In this question, we want to remove the noise from a land cover image. The image called

‘image.jpg’ is provided. The image has some noise, such as English words and numbers, which should be removed before further processing.

1. Read the satellite image and convert it into a grayscale image. Present the color image and the grayscale image.

2. Implement Robust PCA on the grayscale image to obtain the background image (low-rank matrix), and the noise image (sparse matrix). Present both images. The noise should be separated from in the original image.  In the background image, the noise should be blurred or invisible, while the edges of lands are still visible. Please do not use built-in Robust PCA function directly.

3. Do edge detection on the grayscale image and the background image, then calculate the mean squared errors (MSE) and correlation between two edge detected images. Present the two edge-detected images and report the MSE and correlation coefficient (the coefficient should be above 0.5). You may use built-in functions for Canny algorithm or other algorithms to do edge detection.

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