[x, obj] = fista(F_mag, x_init, lambda, pars)
F_mag is the magnitude of the discrete Fourier transform. x_init is the initial guess of the signal. lambda is the weight on the total variation regularization term. pars is a structure with additional parameters: L is the inverse step size in the proximal map. tol is the cutoff for the normed difference between successive iterates in solving the proximal subproblem. If the difference falls below tol, the algorithm terminates. iters is the number of iterations to run FISTA, as well as the maximum number of iterations for the proximal subproblem. bnds is a vector of the lower and upper bounds on the signal. dom is a binary matrix that equals 1 for all pixels in the non-zero support set. tv_type is the type of total variation penalty to use. Must be 'isotropic' or 'anisotropic'.
A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation deblurring and denoising problems.” IEEE Transactions in Image Processing, vol. 18, no. 11, pp. 2419-2434, Nov. 2009.