A Study Of Computational Optical Section Microscopy

At present, there are two main kinds of three-dimensional microscopy technologies. One is laser scanning confocal microscopy (LSCM). Another is computational optical section microscopy (COSM). COSM has the advantages of high signal-noise ratio, non-bleaching and low cost, in spite of the disadvantage of low speed. With the development of computer and image processing, COSM will see more widespread applications in the future. Right now, some researchers have carried out intensive and extensive studies on it and made some progresses. Many algorithms have been proposed, including non-iterative algorithms, such as nearest neighboring, depth prediction and inverse filtering, and iterative algorithms, such as maximum likelihood, EM, PBD and blind restoration. The non-iterative ones are fast in computation but less satisfactory with restoration. In contrast, the iterative ones are better in restoration but slow in computation.The serial images acquired towards depth are blurred and both the noise model and the point spread function of the imaging system are unknown. The key problem in COSM is how to use the theories of signal processing, image restoration and optical information to restore the 3D image of the specimen accurately and quickly from the blurred serial images. Another problem is how to increase the speed of restoration. In this thesis, the author's research work, on the basis of relevant COSM studies, is presented as follows.1. Point Spread Function (PSF) Modeling of Microscopy Imaging System.PSF modeling is very important in image restoration. A three dimensional PSF model was derived from Fresnel's formula of diffraction. The PSF's light intensity distribution was discussed and simulated in both transverse and axial directions. The frequency response of a traditional microscopy imaging system was compared with that of a confocal microscope. In accordance with Nyquist sampling theorem, an expression of a slice spacing in the z direction was derived. A 3D Gauss PSF, which has high applicable value was also derived based on the characteristics of an ideal PSF. The light intensity distribution and the frequency response property of the 3D Gauss PSF approximate those of the ideal PSF. The advantages of it are fewer parameters, less computation and faster image restoration.2. PSF Parameter Estimation.In actual applications, the PSF of a system is usually unknown. This will lead to great computation, slow convergence and uncertain restoration. Therefore, the PSF estimation is of vital importance in image restoration. However, a precise estimation method has not yet been found. Because the PSF of a defocused system can be approximated in a Gauss function, an intensive study on the estimation of the Gauss PSF was undertaken. Based on wavelet transform theory, the relationship of the wavelet's module maximal value, Lipschitz exponent and the variance of the Gauss PSF were determined. A new method was developed for accurate estimation of the Gauss PSF parameters. Experimental results show that using this new method the degree of the accuracy is rather high, and up to 95%. Moreover, the new method can also be applied to the nonsymmetrical PSF estimation as well as to the time and space variant PSF estimation, thus it has a very high applicable value.3. Nearest Neighboring Algorithm DevelopmentIn conventional microscopy 3D imaging, each image acquired contains the information of a focal plane and out of focus planes, so it is blurred. An existingnearest neighboring algorithm was used to restore the information of a focal plane by subtracting that of its neighboring planes from that of the acquired image. The advantages of the algorithm are less computation and faster image restoration. The disadvantage is unstable in restoration of different regions. In actual applications, the inter-plane PSF usually cannot be obtained accurately, so it is replaced by blur function. This leads to unsatisfactory restoration. Therefore, on the basis of the Gauss PSF estimation algorithm, a new predictive algorithm was developed for inter-plane PSF estimation using wavelet theory. The algorithm estimates first the Gauss PSFs of the focal plane and the neighboring planes, respectively. Then it computes the PSF of the inter-plane according to the convolution property of Gauss function. In addition, an improved block division nearest neighboring algorithm was developed to overcome the weaknesses of the existing algorithm. It can reduce the inter-plane bluring intervention. Experimental results show good restoration effects on simulated and practical samples.4. Frequency Domain Based Predictive Depth Algorithm Development According to the characteristics of 3D microscopy imaging, an existingpredictive depth algorithm based on Fourier transformation was analyzed. The algorithm can only predict the single objects with small depth variance. Different from Fourier transformation, wavelet transformation introduces multi-scale definition, thus can detect good local characters in time and frequency domains. It can also focus on arbitrary details of objects to be analyzed. Thus an improved algorithm was developed. The algorithm can compute the depth pixel by pixel based on wavelet decomposition and predict multi-objects with big depth variance.5. Improved Inverse FilteringIn a practical 3D microscopy imaging system, the frequency spectrum of a specimen can be obtained through inverse filtering. The advantage of inverse filtering is less computation. The disadvantage is noise amplification. Based on 2D Wiener filtering, an improved 3D Wiener filtering algorithm and a 3D incrementalWiener filtering algorithm were proposed. The algorithms automatically update signal-noise ratio with respect to frequency change. Experiments demonstrate that the improved algorithm has better restoration capability than conventional Wiener filtering and inverse filtering.6. Statistic Imaging Model Based RestorationBecause imaging can be seen as a random process, an existing statistic imaging model based restoration algorithm was reported. In the algorithm, Poisson distribution was chosen as the statistic imaging model and maximum likelihood are the restoration criterion. It can compensate for some lost frequency components, get better restoration effect, but may lose dark details. On the basis of the statistic image model and detailed analysis of maximum likelihood algorithm, an improved restoration method was proposed to constraint contrast. Because of large computation and data, the newly proposed parametrical blind deconvolution (PBD) algorithm hardly meets the practical restoration demand. After the gradient computation in the algorithm was analyzed, a Gauss PSF based PBD method was developed. Simulating experiments show that the algorithm's computation is simple and convergence is fast.7. Development of Blind Restoration of 3D Microscopy Images. Blind image restoration is one of the hottest subjects in image restoration. The existing maximum likelihood blind restoration algorithms applied to COSM cannot guarantee convergence. This leads to iterative time consumption and unsatisfactory effect. To solve this problem, first, the blind restoration algorithm and the convergent NAS-RIF algorithm were studied thoroughly. Then, an improved algorithm based on image segmentation and wavelet denoise was developed, taking into account of NAS-RIF's disadvantages, such as rectangular but not adaptive supporting region used and poor noise preventing. The developed algorithm can locate the accurate supporting regions of objects and reduce noises. Experiments using the algorithm in 3D microscopy image restoration show satisfactory result.8. Depth variant PSF Restoration StudyIn the practical imaging, the large mismatch in the refractive index of 3D specimen relative to that of immersion medium leads to different PSFs in different depths. In this case, the supposition of invariant PSF will lead to poor restoration. Therefore, after the cause of PSF varying with depth was discussed and the depth-variant imaging model of a 3D optical microscopy section was analyzed, a new maximum likelihood image restoration algorithm was developed based on EM algorithm. Simulating experiments of restoration of a 3D image sequence show that this new algorithm can deblur the blur brought by the varying PSFs and generate good image restoration result.