Microscope is an essential imaging tool. It is commonly used in research labs as well as in the industry. When using microscope for 3D imaging, one encounters an inherent problem.
Abstract
Microscope is an essential imaging tool. It is commonly used in research labs as well as in the industry. When using microscope for 3D imaging, one encounters an inherent problem. The recorded image is blurred, thus significant data is lost. The project’s goal is to estimate the imaging system blur, (referred to as PSF – Point Spread Function) and reconstruct the specimen density. In our project we used a model, brought forth in the article “Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur” written by J. Markham and J. A. Conchello. We implemented the proposed algorithm and evaluated the reconstruction quality.
The problem
When imaging a specimen in a microscope, the recorded image which we mark by g is given by: 
(Where ‘s’ mean specimen & ‘h’ mean PSF) Acquiring the image : The procedure involves the recording of a series of 2D images by focusing the microscope at different planes through the specimen. The resulting batch of 2D optical slices is made up of slices that contain the in-focus plane plus contributions of light from out-of-focus planes that obscure the image and reduce contrast.
The solution
We model the PSF as a function with rather low number of parameters.And as a quality criterion we use the Log(Likelihood) of the recorded emission process. We use a Poisson noise model for the light emission from the specimen. The cost function is Max{L}. The estimation divides to two parts QuasiEstimating the PSF using -Newton algorithm. Estimating the : specimen using EM algorithm, use the two algorithms alternately until We we reach the desirable result.
The Likelihood Function L :
The PSF is given by:
when
The pupil function is given by:
When
We represent 
as:
When the parameters we seek are:
The EM method:
Tools
The project was programmed in Matlab 6 on a pc platform . The main matlab tools were the Image Processing toolbox and optimization toolbox.
Conclusions
In our project we tried several blur functions.Our main conclusion is that the model proposed by the article causes a lot of local maximum points in the cost function, and therefore it is not fit to use with Quasi-Newton algorithm, using this model in the proposed algorithm results bad deconvolution quality. We tested another model where the PSF is Gaussian, with a blur that proportional to the distance from the focal plane.
We had a full process with the physical Gaussian model on a real data. We note that this model is inaccurate approximation of the real PSF but it allows us partial reconstruction. And the reconstructed image is better then the reconstructed image when using the previous model.
Here are the results:
Acknowledgement
We are grateful to our project supervisor Sarit Shwartz for her help and guidance throughout the project. We would also like to thank Dr. Yoav Shechner for his academic support, and at last to the lab staff: Johanan Erez and Ina Krinsky for their technical support.
We are also grateful to the Ollendorff Minerva Center Fund for supporting this project.