Optimization problem, Gradient based method

Good day sirs, I am new to Matlab. I need Matlab for an article. I am currently trying to apply gradient point algorithm for image deblurring. There exists a relationship between the model $\min_{x}F(x)=f(x)+g(x)$ where f is a smooth and convex function and $g$ is necessarily not smooth and the inclusion problem . The algorithm for solving the latter could be extended to the former. A well known model for the former is the linear inverse problem . Where τ >0 is a regularization method. The gradient method defined by is a well known algorithm for solving the problem . My problem is how to apply this model for image deblurring and writing the source codes for it. Any help will be appreciated. Thanks