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13 July 2004 Reconstruction of objects with a limited number of non-zero components in fluorescence microscopy
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A reconstruction algorithm is developed that uses specific a-priori knowledge to produce higher resolution images than standard approaches. Deconvolution is an important image reconstruction tool in fluorescence microscopy. This is especially true for modern interferometric instruments (such as I5M and 4Pi systems), as they may have complicated oscillatory point spread functions. Current methods are designed to work on an arbitrary object - i.e. it is assumed that there is no available a-priori knowledge of the object (with the possible exception of a non- negative condition on the fluorophore-emission intensities). In situations where there is a-priori knowledge of the object, it may be possible to use this information to produce a higher quality reconstruction of the object. A useful a-priori condition is investigated here. It is assumed that the object can be represented by the sum of not more than L basis functions. The simplest example of this is when the basis functions are impulses - this leads to an object of L or less non-zero points on a background of zeros. This a-priori condition can be applied directly; applied to a limited region of the object; applied in one dimension (for an object with a layered structure such as lipid bilayers); or applied in two dimensions (for an object with a filamentary structure such as actin fibers.) A reconstruction algorithm is described and applied to some illustrative simulated examples. The results are found for several fluorescence microscopy methodologies and compared to the results produced by standard deconvolution methods.
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Brynmor J. Davis, William C. Karl, Anna K. Swan, Bennett B. Goldberg, M. Selim Unlu, and Marcia B. Goldberg M.D. "Reconstruction of objects with a limited number of non-zero components in fluorescence microscopy", Proc. SPIE 5324, Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XI, (13 July 2004);

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