PhD position: Optimal correlations

Concurrent localisation in the position and wavelength of any object is constrained by the Heisenberg Uncertainty Principle. Real world applications that seek to maximise such localisation aspects range from synthetic aperture imaging to watermarking digital media. They often rely on the construction of discrete signals with ‘all or nothing’ properties: an embedded signal is either exactly locatable to within a single pixel position or they remain completely transparent to a large range of probe signals.

This project examines methods to construct large families of discrete signals that have maximal and/or minimal correlations between family members. A recently discovered class of such signals has been extended from binary to multivalued functions. Ideally, these multivalued signals will retain their ‘perfect’ properties when constructed using purposefully chosen combinations of values (for example functions that have a uniformly flat or linear histogram of grey values). A related goal is to investigate ‘ghosts’ in N-dimensions. These are N-dimension signed discrete functions whose projected views in less than N dimensions are exactly zero across the full width of the domain they occupy. A longer term goal is to construct compact N-dimensional functions that have optimal correlations and retain the zero sum property.