Solve the diffusion PDE in Isotropic linear diffusion smoothing using Python

Question

I want to apply the de-noising filter using linear diffusion smoothing which is based on the following equations: where d = 1 is a scalar constant diffusivity parameter, I(x, y) is the initial noisy image, and u(x, y, t) is the image obtained after a diffusion time t lets say 1, 5, 10, 30 and 100. The code is obscure to me here. What type of boundary conditions should I choose here?

here is the sample image Noisy office Image