Reconstruction of objects with a limited number of non-zero components in fluorescence microscopy

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 I-5 M 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.