Computer Vision (URGENT): Please answer all parts and SHOW WORK for equations or provide a python script, thanks! (will upvote :))

STEPS

To perform principal component analysis (PCA) on six multispectral satellite images, you can follow these steps:

Organize the images so that each set of corresponding pixels in the images forms a six-element vector x. The population of vectors will consist of 65536 vectors (256x256 pixels). Compute the mean vector m_x, which is the expected value of x, and the covariance matrix C_x, which is the expected value of the outer product of x minus the mean vector. Compute the eigenvalues and eigenvectors of C_x. The eigenvectors can be used as rows of a matrix A. Using A, compute a set of y vectors according to y = A(x - m_x). Compute the covariance matrix C_y of y as C_y = AC_xA^T, which is a matrix with diagonal elements as the eigenvalues of C_x.

IMAGES

PCA analysis (30\%): For six multispectral satellite images corresponding to six spectral a. please organize the images that leads to the formation of a six-element vector x from each set of corresponding pixels in the images (256256), so the population consisted of 2562=65536 vectors from which the mean vector mx=E{x}, covariance matrix Cx=E{(xmx)(xmx)T}, and corresponding eigenvalues and eigenvectors can be computed. b. using eigenvectors as rows of matrix A, compute a set of y vectors according to y= A(xmx). Similarly compute Cy=ACxAT which is a matrix with diagonal elements as eigenvalues of Cx. c. generate a set of six principal component images using the y vectors, notice the significant portion of the contrast detail is contained in the first two images and decreases rapidly from there