3. Project using MATLAB) Make your own MATLAB code for compressing an imaging file using SVD. The source code annotation as 4) should be essentially included in your own m-file. You should submit the reports for this MATLAB project with m-file in cyber campus. (100 pt + 50pt (bonus points)) (1) The program for compressing the gray scale-image according to singular values. Your code should include the following contents: First, load your own image (your photo etc.) and convert the colored image to the gray-scale image and make a matrix for the gray-scale image. Then, cut off the matrix according to singular values, and store and show the compressed gray-scale images. Select the singular values that correspond to 5.10.20.30. and 50% of the total numbers of singular values. (60 pt) (2) Evaluate the approximation errors between the original gray-scale matrix and the compressed matrix with respect to the number of singular values. The error is defined by Frobenius Norm. Using the regression (linear or nonlinear), draw the estimated equation between the errors and the number of singular values. Verify the equation with some points that are not used in the regression. (20 pt) (3) Induce the estimated equation for the relation between the compressed file size and the number of singular values using the regression. Verify the equation with some points that are not used in the regression. If you want to compress your photo file into 25% of its original size, how many numbers of singular values should be used? (20 pt) (4) Upgrade your compression program for colored images using SVD. (50 bonus points) 3. Project using MATLAB) Make your own MATLAB code for compressing an imaging file using SVD. The source code annotation as 4) should be essentially included in your own m-file. You should submit the reports for this MATLAB project with m-file in cyber campus. (100 pt + 50pt (bonus points)) (1) The program for compressing the gray scale-image according to singular values. Your code should include the following contents: First, load your own image (your photo etc.) and convert the colored image to the gray-scale image and make a matrix for the gray-scale image. Then, cut off the matrix according to singular values, and store and show the compressed gray-scale images. Select the singular values that correspond to 5.10.20.30. and 50% of the total numbers of singular values. (60 pt) (2) Evaluate the approximation errors between the original gray-scale matrix and the compressed matrix with respect to the number of singular values. The error is defined by Frobenius Norm. Using the regression (linear or nonlinear), draw the estimated equation between the errors and the number of singular values. Verify the equation with some points that are not used in the regression. (20 pt) (3) Induce the estimated equation for the relation between the compressed file size and the number of singular values using the regression. Verify the equation with some points that are not used in the regression. If you want to compress your photo file into 25% of its original size, how many numbers of singular values should be used? (20 pt) (4) Upgrade your compression program for colored images using SVD. (50 bonus points)