Singular Value Decomposition (SVD) is a powerful idea from linear algebra which aims to extract useful information about a matrix. We can gain insight to the significance of the SVD in regards to low-rank approximations to matrices by considering a digital image as an mxn matrix. The entries are just the brightness of the corresponding pixel. The values range from 0 (black) to 1 (white) and colors are of course also possible. Instead of storing full images, we often compress them to store less information, which can be achieved with the SVD and low rank approximations. Problems Your task is to write two MATLAB codes, one for in-built image in MATLAB and another one for any image of your choice (to be loaded into your code) and generate two matrices for each image called H and H respectively. Then do the following: 1. Compute and display rank, k of H and r of H2 (use the rank function). 2. Compute the singular value decomposition of H and H2 (use the svd function). 3. Use four different values of ranks of H and H2 (k, k2, k3, k4 and r1, T2, T3, T4) to process the images and display the corresponding images. You will need to report the rank in the title of the corresponding figure. Organize your images in a 3 2 grid using subplots (Recall MATLAB's subplot command). Include the original image as well. 4. Also, in a separate figure, make a plot of singular values of H and H2 to see how the size of singular values drop at some point (this gives you an idea of for what rank should be to get a reasonably close to original image). Use plot (diag(S)) for the plot of singular values. 5. How can you relate the quality of what you see to the singular values of H and H2 and the approximations you are generating? Organize your work in the following way: (a) All codes must be saved starting with student's last name such as lastname_image_proc_image1.m. (b) All codes should be well written and explained to aid reading. (c) Write a short report for both images to discuss what you observe. (d) Generate all the plots to include them in your report. (e) All plots should be titled and labeled. Assignment should be submitted as a single pdf file (with report on the first page, followed by all the plots and finally the codes at the end) and all codes separately uploaded. This Mini-Project 3 should be submitted directly in Moodle (save files starting with last name of student).