Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...144..381t&link_type=abstract
Astronomy and Astrophysics, Vol.144, NO.2/MAR(II), P. 381, 1985
Astronomy and Astrophysics
Astrophysics
62
Scientific paper
Regularization procedures are portrayed as compromises between the conflicting aims of fidelity with the observed image and perfect smoothness. The selection of an estimated image involves the choice of a prescription, indicating the manner of smoothing, and of a smoothing parameter, which defines the degree of smoothing. Prescriptions of the minimum-penalized- distance type are considered and are shown to be equivalent to maximum-penalized-smoothness prescriptions. These include, therefore, constrained least-squares and constrained maximum entropy methods. The formal link with Bayesian statistical analysis is pointed out. Two important methods of choosing the degree of smoothing are described, one based on criteria of consistency with the data and one based on minimizing a risk function. The latter includes minimum mean-squared error criteria. Although the maximum entropy method has some practical advantages, there seems no case for it to hold a special place on philosophical grounds, in the context of image reconstruction.
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