Algorithm 1.

FLIS algorithm

1:	Input: Y, Ŷ, H, ρ, β, dictionary size K
2:	Output: D, W
3:	procedure FLIS
4:	Find L and an initial value for D using Eq. (9) and Eq. (10)
5:	Find X and X̂ using Eq. (11)
6:	Initialize W using Eq. (12)
7:	Update $Y_{\mathit{new}}=\left(\begin{array}{c}Y\\ \sqrt{\beta }H\end{array}\right),{\widehat{Y}}_{\mathit{new}}=\left(\begin{array}{c}\widehat{Y}\\ \sqrt{\beta }\stackrel{\sim }{H}\end{array}\right),D_{\mathit{new}}=\left(\begin{array}{c}D\\ \sqrt{\beta }W\end{array}\right)$
8:	Update X, X̂ using Eq. (13)
9:	while not converged do
10:	Fix X, X̂ and calculate $E=\frac{1}{N}{Y}_{\mathit{new}}{X}^T-\frac{\rho }{\widehat{N}}{\widehat{Y}}_{\mathit{new}}{\widehat{X}}^T;F=\frac{1}{N}X{X}^T-\frac{\rho }{\widehat{N}}\widehat{X}{\widehat{X}}^T$
11:	Update Dnew by solving
	$arg\underset{D_{\mathit{new}}}{min}\{-2\text{trace}(E{D}_{\mathit{new}}^T)+\text{trace}(D_{\mathit{new}}F{D}_{\mathit{new}}^T))\}$
12:	Fix Dnew, find X and X̂ using Eq. (13)
13:	end while
14:	end procedure
15:	RETURN: Dnew