Image  Means of Producing Superresolved Binary Images Through Bandlimited Systems.
Abstract
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, shiftinvariant, 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 highcontrast 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 realvalued functions and for the class of complexvalued 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 spacebandwidth 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 onedimensional 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 infiniteresolution is not always possible for twodimensional 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 zerocrossing locations and interpolating a twodimensional function from the slices. Another method uses polynomials to define the desired zerocrossing contours of a twodimensional bandlimited function. In these methods, as well as in the iterative methods, it is shown that superresolution can be achieved.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 1987
 Bibcode:
 1987PhDT........54N
 Keywords:

 Physics: Optics