Digital Image Restorations: Algorithms and Accuracy with Applications to Astronomical Observations

Details Digital Image Restorations: Algorithms and Accuracy with Applications to Astronomical Observations Digital Image Restorations: Algorithms and Accuracy with Applications to Astronomical Observations

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........4z&link_type=abstract

Thesis (PH.D.)--TUFTS UNIVERSITY, 1995.Source: Dissertation Abstracts International, Volume: 56-05, Section: B, page: 2801.

Computer Science

Performance

Wiener Filters, Deconvolution

Scientific paper

This work addresses the problem of restoring degraded images and assigning confidence intervals to the resulting restorations. A new approach for constructing a class of iterative restoration techniques is presented. A set of multiplicative restoration algorithms, one of which is the Richardson-Lucy algorithm, is described for constructing positively constrained maximum likelihood estimates from data modeled by either Poisson or Gaussian processes. These deconvolution techniques provide a method for describing and accelerating the rate of convergence of known methods and for developing new iterative algorithms. They positively constrain the output space by re-mapping the parameters with either exponential or monomial functions. In conjunction with this work, a general method was developed for calculating the confidence on each estimate produced by not only this class of restoration techniques but by other linear approaches. This method uses the Cramer -Rao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. Compact and simple forms are presented for the bounds associated with estimates constructed via linear processes such as Wiener filters, and iterative techniques like the Richardson-Lucy algorithm. These prescriptions for estimating the variance associated with each element in a restored object are developed for observed data corrupted by either Poisson or Gaussian noise. Multiple 1-D and 2-D examples are presented to describe the performance of this new class of iterative restoration techniques, but also to illustrate the formation of these bounds. Finally, a set of calculated bounds are shown for Wiener filter estimates of gravitational lenses. These Wiener filter restorations and bounds are based on Hubble Space Telescope data of multiply imaged quasars.

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