MRI TV-Rician Denoising - Biomedical Engineering Systems and Technologies - page 239

Fig. 2. Energy in functional 6 of the solution obtained at each step of the gradient descent by
the approximated method for λ =0 . 1 , σ =0 . 05 , τ =0 . 001 and different values of =
10 − 1 , 10 − 3 , 10 − 5 , 10 − 7 , and by the new method for λ =0 . 1 , σ =0 . 05 , τ =0 . 001

(a) Existing method (b) Proposed method

Fig. 3. Absolute difference between the original image and the solution of the existing method
and the proposed method for the values λ =0 . 1 , σ =0 . 05 , τ =0 . 001 in both methods and
=10 − 7 for the approximated method

when completely different initial condition are used for initialization in the gradient
flow schemes we considered. This is suggestive of uniqueness for the non trivial solu-
tion of the corresponding elliptic problems.