Algorithm 1.

Proposed algorithm for the recovery of exponential image time series

Initialize ρ̂(0) and choose ε(0) > 0;
for n = 1 to Nmax or tolerance threshold reached do
	Step1: Weight matrix update:
	Compute each block Rp,q of the Gram matrix R using (28) and (29);
	Compute the eigen values and eigen vectors ${\{{\lambda }^{(i)},{\mathbf{u}}^{(i)}\}}_{i=1}^M$ from the eigen decomposition of R;
	Evaluate the null space vectors: $${\mathbf{h}}^{(i)}=\sqrt{{\alpha }_i}{({\mathbf{u}}^{(i)})}^{\ast },\text{where}$$ $${\alpha }^{(i)}={({\lambda }^{(i)}+{\epsilon }^{(n-1)})}^{\frac{p}{2}-1};$$
	Step2: Least Squares update:
	Solve the least squares problem: $${\hat{\mathit{\rho }}}^{(n)}={\text{agr min}}_{\hat{\mathit{\rho }}}{\sum }_{i=1}^M{\Vert \mathbf{D}({\mathbf{h}}^{(i)}){\mathbf{Q}}^{\ast }\hat{\mathit{\rho }}\Vert }_2^2+\frac{\mu p}{2}{\Vert 𝒜(\hat{\mathit{\rho }})-\mathbf{b}\Vert }_2^2$$ using Conjugate gradient (CG) method;
	Choose ε(n) such that 0 < ε(n) ≤ ε(n−1);
end