min TV(u,&tau) + 0.5*&mu*||u-h||2where the first term is a smoothed total variation of image u that depends on a smoothing parameter &tau, and the quantity h in the second term is a given noisy image. We have implemented a simple nonlinear conjugate gradient (NCG) method for minimizing the function. The purpose of the project is to familiarize yourselves with image denoising and an optimization algorithm involved. The algorithm uses a back-tracking line search to choose step length. The stopping criterion is either
crit := norm(g)/(1 + abs(f)) < tol;or the maximum iteration number maxit is reached.
Download the zipped file proj1.zip and open it. Study the codes to know who does what (a thorough understanding is not necessary though). Run the test script test1.m (you will need image processing toolbox).
Your task is to start from mysolve0.m and modify it into mysolve.m so that it can perform as well as, or better than, the instructor's code zysolve.p for the given parameter values (i.e., &tau = tol = 1.e-5). As it is, mysolve0.m is much slower. The trick is to gradually decrease &tau value. Also experiment with different values for &mu to see its effect.
Submit your code, printout including graphs, and a short, and typed, report that explains what you have done and observed.