English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is well-known that the noise associated with the collection of anastronomical image by a CCD camera is, in large part, Poissonian. One wouldexpect, therefore, that computational approaches that incorporate this a prioriinformation will be more effective than those that do not. The Richardson-Lucy(RL) algorithm, for example, can be viewed as a maximum-likelihood (ML) methodfor image deblurring when the data noise is assumed to be Poissonian.Least-squares (LS) approaches, on the other hand, arises from the assumptionthat the noise is Gaussian with fixed variance across pixels, which is rarelyaccurate. Given this, it is surprising that in many cases results obtainedusing LS techniques are relatively insensitive to whether the noise isPoissonian or Gaussian. Furthermore, in the presence of Poisson noise, resultsobtained using LS techniques are often comparable with those obtained by the RLalgorithm. We seek an explanation of these phenomena via an examination of theregularization properties of particular LS algorithms. In addition, a carefulanalysis of the RL algorithm yields an explanation as to why it is moreeffective than LS approaches for star-like objects, and why it provides similarreconstructions for extended objects. We finish with a convergence analysis ofthe RL algorithm. Numerical results are presented throughout the paper. It isimportant to stress that the subject treated in this paper is not academic. Infact, in comparison with many ML algorithms, the LS algorithms are much easierto use and to implement, often provide faster convergence rates, and are muchmore flexible regarding the incorporation of constraints on the solution.Consequently, if little to no improvement is gained in the use of an MLapproach over an LS algorithm, the latter will often be the preferred approach.Comment: High resolution images are available upon request. submitted to A&

Least-squares methods with Poissonian noise: Analysis and comparison with the Richardson-Lucy algorithm