Algorithm 1 On-line hyperspectral dictionary learning algorithm.

$\mathbf{Initialization}:$ Taking the HS reflectance of all pixels in the observed LR-HS image as the HS sample set $\left\{S\right\}$, initialize dictionary set $\mathbf{B}$ as $\left\{\varphi \right\}$, and set the correlation similarity threshold $\theta$;

1. Randomly select an HS reflectance ${\mathbf{s}}_t$ as temporary set $\left\{S^t\right\}=\left\{{\mathbf{s}}_t\right\}$ from $\left\{S\right\}$, and update $\left\{S\right\}$ by removing ${\mathbf{s}}_t$;

2. Calculate the normalized correlation coefficients $r_i$ between ${\mathbf{s}}_t$ and any sample ${\mathbf{s}}_i$ in $\left\{S\right\}$:

$r_i=\frac{{\sum }_{l=1}^L{s}_{t,l}{s}_{i,l}}{\sqrt{{\sum }_{l=1}^L{s}_{t,l}}\sqrt{{\sum }_{l=1}^L{s}_{i,l}}}$

If $r_i>\theta$, we take ${\mathbf{s}}_i$ from $\left\{S\right\}$ into $\left\{S^t\right\}$ $\left\{S\right\}{\Rightarrow }^{{\mathbf{s}}_i}\left\{S^t\right\}$.

3. Repeat the same process for all samples in $\left\{S\right\}$

4. Calculate the mean vector in $\left\{S^t\right\}$ as the HS basis ${\mathbf{b}}_t$; put it into the dictionary $\mathbf{B}$ ${\mathbf{b}}_t\Rightarrow \mathbf{B}$; and re-set $\left\{S^t\right\}$ as $\varphi$.

6. If $\left\{S\right\}$ is $\varphi$, finish; otherwise go to Step 1.