Image Deconvolution with Uncertainty Estimates: Hierarchical Multiscale Models for Poisson Images

Details Image Deconvolution with Uncertainty Estimates: Hierarchical Multiscale Models for Poisson Images Image Deconvolution with Uncertainty Estimates: Hierarchical Multiscale Models for Poisson Images

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aas...201.6303e&link_type=abstract

American Astronomical Society, 201st AAS Meeting, #63.03; Bulletin of the American Astronomical Society, Vol. 34, p.1214

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Have you ever wished you could obtain error maps for image deconvolutions? The work described here, currently under development, provides a method for doing exactly this. Also, the procedures described here can effectively restore point or extended sources, and there is little tuning necessary on the part of the user. We will first survey the currently used methods for image restoration. Our method models images as Poisson processes, the pixel intensities equal to the true image intensities convolved with the PSFs. The true image intensities are modeled as a mixture of point sources and a Haar Wavelet decomposition of the remaining image. The point sources are modeled as small circular Gaussian densities with fixed location, assigned by the user. The particular wavelet decomposition of the remaining image is the only one which allows the Poisson likelihood to be factored into separate parts, corresponding to the wavelet basis, ranging from coarse to fine resolution. Each of these factors in the likelihood can be reparametrized as a split of the intensity from the previous, coarser factor. We assign a prior to these splits, which can be viewed as smoothing parameters, and then fit the model using Markov Chain Monte Carlo (MCMC) methods. This fitting method allows for lower levels of smoothing on the image, and is desirable for our model because we are trying to effectively summarize, not simply maximize, the density. Our method largely automates the choice of tuning parameters in the model, and therefore makes the procedure largely user-independent. It also produces information about the certainty of the estimates; which can be summarized with error maps, or multiple images showing the variability of the posterior distribution. Our procedure has an additional strength in that it can effectively handle extended sources, without shrinking them down to a few localized points. Simulations and examples using real data will be presented and compared with other deconvolution techniques. Reference: Nowak, R.D. and Kolaczyk, E.D. (2000). A Bayesian Multiscale Framework for Poisson Inverse Problems. IEEE Transactions on Information Theory, 46:5 1811-1825.

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