Image - Means of Producing Superresolved Binary Images Through Bandlimited Systems.

It is desired to preprocess an input image so that when it is distorted by an imaging system a prescribed output image is produced. The system of interest is a linear, shift-invariant, bandlimited system followed by a hardlimiter. Such a system is found, for example, in microphotography, when a camera that is bandlimited by diffraction effects is used to print on very high-contrast film. A number of approaches to solving this problem are developed. In the first approach solutions are found using a method of alternating projections, first onto the set of bandlimited functions, then onto a set of functions with magnitudes above and below the threshold of the hardlimiter in the appropriate regions. The process is repeated iteratively until a function is found with both desired properties. This was done both for the class of real-valued functions and for the class of complex-valued functions. It was found that enlarging the class of allowed inputs to include complex -valued functions, rather than restricting them to be real -valued, resulted in solutions for problems with smaller space-bandwidth products. An alternate approach involves examining the zero crossings of bandlimited functions. Given a set of prescribed zeros within an interval of finite extent, a one-dimensional bandlimited function can always be found that has those and only those zeros, within the interval. This can be done by replacing zeros in a sinc function or other known bandlimited function. Such infinite-resolution is not always possible for two-dimensional functions. In this thesis, however, it is shown that the desired results can be approximated arbitrarily closely. One method relies on producing one -dimensional slices which have the desired zero-crossing locations and interpolating a two-dimensional function from the slices. Another method uses polynomials to define the desired zero-crossing contours of a two-dimensional bandlimited function. In these methods, as well as in the iterative methods, it is shown that superresolution can be achieved.