Algorithm 1: LOCALIZATION([in] Ik (x) [out] ˆI(X)).

$$\begin{array}{cc}\hfill & \mathbf{Input}:(i)I_k(\mathbf{x})-\text{The intensity of the frame}k\text{for}\hfill \\ \hfill & 1\le k\le K\text{in resolution-limited image}.\hfill \\ \hfill & \mathbf{Output}:\widehat{I}(\mathbf{X})-\text{Estimated intensity in super-resolution}\hfill \\ \hfill & \text{image}.\hfill \\ \hfill & 1:\mathbf{for}l=1:L\mathbf{do}\hfill \\ \hfill & \mathbf{a}.\text{Fit a 3D Gaussian function to}{I}_k(\mathbf{x})\text{usign least}\hfill \\ \hfill & \text{squares optimization based on Levenberg-Marquardt}\hfill \\ \hfill & \text{algorithm, yielding the coordinates}{x}_c,y_c,z_c.\hfill \\ \hfill & \mathbf{b}.\text{Find the uncertainty of the position}{\sigma }_x,{\sigma }_y,{\sigma }_z\hfill \\ \hfill & \text{using all}K\text{frames}.\hfill \\ \hfill & \mathbf{c}.\text{Position mapping of the Gaussian-formed image}\hfill \\ \hfill & \text{into high resolution image using}\hfill \\ \hfill & I_l(\mathbf{X})=\frac{A}{2\pi {\sigma }_x{\sigma }_y{\sigma }_z}\text{exp}\hfill \\ \hfill & \left(-\left(\frac{({\mathbf{X}}_l-{\mathbf{x}}_c{)}^2}{2{\sigma }_x^2}+\frac{({\mathbf{Y}}_l-{\mathbf{y}}_c{)}^2}{2{\sigma }_y^2}+\frac{({\mathbf{Z}}_l-{\mathbf{z}}_c{)}^2}{{\sigma }_z^2}\right)\right).\hfill \\ \hfill & 2:\mathrm{end}\mathrm{for}\hfill \\ \hfill & 3:\text{Combine the single bubble high resolution images}\hfill \\ \hfill & I_l(\mathbf{X})\text{for 1}\le l\le L\text{into a composite image using}\hfill \\ \hfill & \text{maximum intensity projection method}.\hfill \end{array}$$