Noise reduction in astronomical spatial spectrum measurements

Object constraints, or "prior knowledge," can be powerful tools in image reconstruction algorithms. An example of such a constraint is knowledge of the object "support," or angular extent in the field. In the work reported here, I analyze and demonstrate the use of image support constraints in a noise-reduction algorithm.; Previous work has revealed serious limits to the use of support if image noise is wide-sense stationary in the frequency domain; I use simulation and numerical calculations to show these limits are removed for nonstationary noise generated by inverse-filtering adaptive optics image spectra. To quantify the noise reduction, I plot fractional noise removed by the proposed algorithm over a range of support sizes and for other noise sources with varying degrees of stationarity.; Support constraints remove noise by inducing noise transport between bands in image data spectra. I discuss why this phenomenon can be particularly effective at removing noise from aperture synthesis data, such as that collected by interferometer arrays or aperture-masked telescopes. I also present simulation results demonstrating noise removal in a synthesis experiment.; I also discuss an algorithm to increase the energy spectrum SNR of astronomical image data, with application to the technique of speckle interferometry and binary star analysis. This method, again using support a support constraint, can result in one or both of two phenomena; noise scaling and noise transport. The effects of these two phenomena are discussed and analyzed. I show that noise scaling can be quantified using a simple integral, and can result in increased sensitivity to faint companions if spectral SNR increases are taken into account when filtering. Noise transport can be understood using a more complicated diffusion model, and can be used to effect noise reduction inside the object support boundary, again increasing sensitivity to faint companions. I present results using a Fortran 90 implementation of the algorithm on simulated telescope image data, demonstrating significant SNR increases in detector-noise and atmospheric noise-limited data. Finally, I present results using the algorithm with simulated binary star data and demonstrate increased sensitivity to faint companions and increased accuracy in differential photometry.