Subpixel resolution in maximum likelihood image restoration

A number of algorithms have been developed for three-dimensional (3D) deconvolution of fluorescence microscopical images. These algorithms use a mathematical-physics model for the process of image formation and try estimate the specimen function, i.e. the distribution of fluorescent dye in the specimen. To keep the algorithms tractable and computational load practical, the algorithms rely on simplifying assumptions, and the extent to which these assumptions approximate the actual process of image formation and recording has a strong effect on the capabilities of the algorithms. The process of image formation is a continuous-space process, but the algorithms must be implemented using a discrete-space approximation to this process and render a sampled specimen function. A commonly-used assumption is that there is one pixel in the specimen for each pixel in the recorded image and that the pixel size in the recorded image is small compared to the size of the diffraction limited spot or Airy disk, a condition necessary to satisfy Nyquist sampling criterion. Modern CCD cameras, however, have large wells that integrate into a single pixel an area of the image that is significantly larger that the Airy disk. We derived a maximum-likelihood-based algorithm to accommodate for these large CCD pixel sizes. In this algorithm we assume that each pixel in the recorded image integrates several pixels that satisfy Nyquist criterion. The algorithm then attempts to estimate the specimen function at a resolution better than that allowed by the CCD camera. Preliminary results of this sub-pixel resolution algorithm are encouraging.