A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

Paul Salama

doi:10.1117/12.764919

26 February 2008 A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

Paul Salama

Author Affiliations +

Proceedings Volume 6814, Computational Imaging VI; 68140U (2008) https://doi.org/10.1117/12.764919
Event: Electronic Imaging, 2008, San Jose, California, United States

Abstract

Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.

Citation Download Citation

Paul Salama "A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy", Proc. SPIE 6814, Computational Imaging VI, 68140U (26 February 2008); https://doi.org/10.1117/12.764919

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