# Image (De)Convolution

Our collaborators require deconvolution of 3D fluorescence images of yeast biofilms and fibrin clots so that mesh-extraction code (which assumes isotropic tubes) can effectively determine its branching structure. The PRISM system acquires two sets of 3D images at the same time, one from the front and one from the side; this enables the development of a novel 2-directional deconvolution algorithm to achieve high spatial resolution in all three directions at once.

As the figure above shows, fluorescence microscopy produces images of sub-micron structures that are convolved with the Point-Spread Function (PSF) of the microscope, which blurs the image in complicated 3D ways. Responding to our collaborators, we continue to develop tools to address this issue. There are three aims, one associated with doing forward convolution (useful in SketchBio), one associated with removing the effect of convolution (useful in PRISM), and one associated with determining a noise-free estimate of the point-spread function required to do each of these.

**Fluorescence Simulation:***Given a proposed model of fluorophore distribution in a specimen and an estimate of the point-spread function of the microscope used in an experiment, simulate a 3D image stack of the specimen. Given a parameterized model, optimize the parameter settings to minimize the difference between the simulated model and an experimental image.***Deconvolution:***Given one or more 3D image stacks from a microscope scan of a specimen and an estimate of the point-spread function of the microscope, rapidly produce a sharpened image that estimates the actual specimen fluorophore distribution.***Point-Spread Function Estimation:***Given one or more sampled 3D image stacks of a small fluorescence bead in a microscope, produce a noise-free estimate of the microscope’s point-spread function.*