Algorithm 1 The proposed method

1: Input: the PAN image P and the HS image H oversampled to the size of P.

2: Initialize:the pansharpened image $u^0 = H$. Fixed ∆t, γ, η and μ

3: Compute $D_H$ following Equation (5).

4: Obtain Z by GSA

5: for k = 1, 2, …, N

6:  for i = 1, 2, …, n

7:   for pixel x ∈ Ω

8:     Compute Du following Equation (5).

9:    for pixel y ∈ I

10:     Compute the weights w(x, y) following Equation (7).

11:    end for

12:    Compute the iterative scheme in Equation (17)

13:   end for

14:  end for

15: end for

16: u = uk + 1.

17: OUTPUT: pansharpened image u.