Study On Super-resolution Image Reconstruction Algorithms Based On Compressed Sensing For Single-molecule Localization Microscopy

Single Molecule Localization Microscopy(SMLM),such as photoactivated localization microscopy(PALM)and stochastic optical reconstruction microscopy(STORM),is one major family of super-resolution imaging techniques.It utilizes sequential activation and time-resolved localization of photoswitchable fluorophores to achieve high spatial resolutions of 10-20 nm laterally and 20-50 nm axially.It has become a powerful research tool in observing and studying fine structures and functions of cells at the single molecule level,and greatly promoted the developments of life science.However,SMLM usually requires large number of raw frames to reconstruct final high resolution images,which makes SMLM an inherently “slow” technique not only in imaging itself,but also in image processing,thereby limiting its potential for dynamic imaging in living cells.For real-time imaging of fine structures in living cells,SMLM faces two challenges,i.e.improving temporal resolution and reducing the calculating time of localization algorithms.Recent research indicates that compressed sensing(CS)can effectively improve this temporal resolution by realizing localizations of densely distributed molecules.Therefore,this thesis mainly investigated fast super-resolution reconstruction algorithms based on CS.What have done in this thesis is listed as follows:1)Fundamental theory of single molecule localization(SML)algorithms based on CS was studied.Three different high-density SML algorithms based on CS were compared and analyzed.In the CS model,the observation matrix is designed from the point spread function(PSF).Three algorithms based on CS,including the interior point method in the freeware package CVX,the homotopy method and the orthogonal matching pursuit(OMP)algorithm,were investigated.The identified density,localization precision and execution time of these algorithms were compared by simulations and experiments.The simulated results showed that CVX and homotopy methods are better in localization precision at the high molecule densities,but CVX method require more executing time.And the OMP and homotopy methods are one order of magnitude faster than CVX method,but the OMP has lower localization precision at high density case.2)A three-dimensional(3D)localization algorithm for high-density localization was proposed.After a cylindrical lens was introduced to the traditional fluorescence microscope,the observation matrix based on CS model was established with generated 3D point spread function(PSF).Compared with 3D-DAOSTORM,the 3D-CS algorithm can realize the 3D fluorescence molecular localization at 4-5 times higher molecule densities.3)A frequency domain CS algorithm(FD-CS)was developed.The collected images can be converted into frequency domain as the observed values,and a Fourier dictionary constructed in the frequency domain instead of the observation matrix in the spatial domain.FD-CS significantly reduced the computational time of CS-CVX by more than 3 orders of magnitude and that of L1-H by one order of magnitude.4)The results of the above localization algorithms were verified by experimental data.The 2D and 3D experimental data were collected by the homemade STORM platform.The molecules were localized in3 D with 3D CS as expected.Furthermore,the FD-CS was also successfully implemented to reconstruct the final super-resolved image with one order of magnitude faster computing speed than traditional CS algorithms.In this thesis,the main innovations are as follows:1)The CS based on OMP algorithm was used in SMLM.Compared with CS-CVX,this algorithm can not only keep the high localization accuracy,but also improve the computing speed of high density active molecules localization by about 15 times.2)3D localization of molecules with 4-5 times higher density was accomplished by 3D-CS based on 3D astigmatic PSF by adding a weak cylindrical lens to the imaging path in STORM.3)A rapid SML algorithm based on frequency domain CS was proposed.Fourier dictionary was established in frequency domain,replacing observation matrix in spatial domain.OMP algorithm was implemented for the frequency domain CS.This new algorithm is about three orders of magnitude faster than the CS-CVX algorithm in spatial domain and three orders of an order of magnitude faster than the L1-H algorithm in spatial domain.