An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon meth...

This lecture explores the application of pixon-based methods to the reconstruction of complexly encoded images. The special problems sometimes associated with complexly encoded data sets, i.e. an extremely complex and convoluted solution space, are discussed, and numerical methods for dealing with these problems, e.g. simulated annealing, genetic algorithms, and evolutionary programing, are pre...

The Pixon method is a high-performance, nonlinear image reconstruction method that provides statistically unbiased photometry and robust rejection of spurious sources. Relative to other methods, it can increase linear spatial resolution by a factor of a few and sensitivity by an order of magnitude or more. All of these benefits are achieved in computation times that can be orders of magnitude f...

We studied the evolution of two small flares (GOES class C2 and C1) that developed in the same active region with different morphological characteristics: one is extended and the other is compact. We analyzed the accuracy and the consistency of different algorithms implemented in RHESSI software to reconstruct the image of the emitting sources, for energies between 3 and 12 keV. We found that a...

A pixon-based reconstruction imaging method is applied to CGRO COMPTEL data for Viewing Period 3. The eld-of-view of VP3 contains both the AGN sources 3C273 and 3C279 which are about 10 apart. The pixon technique is able to determine the uxes and locations of a number of discrete sources within close proximity to each other. Fluxes and upper limits have been determined for both sources in the t...

We compare the photometric accuracy of spectra and images in flares observed with theRamaty High Energy Solar Spectroscopic Imager (RHESSI) spacecraft. We test the accuracy of the photometry by comparing the photon fluxes obtained in different energy ranges from the spectral-fitting software SPEX with those fluxes contained in the images reconstructed with the Clean, MEM, MEMVis, Pixon, and For...

In the scope of medical image processing, segmentation is important and difficult. There are still two problems which trouble us in this field. One is how to determine the number of clusters in an image and the other is how to segment medical images containing lesions. A new segmentation method called DDC, based on difference of mutual information (dMI) and pixon, is proposed in this paper. Exp...

This lecture reviews the image restoration/reconstruction problem in its general setting. We ̄rst discuss linear methods for solving the problem of image deconvolution, i.e. the case in which the data is a convolution of a point-spread function and an underlying unblurred image. Next, non-linear methods are introduced in the context of Bayesian estimation, including MaximumLikelihood and Maximum...

[1] In the early 1980s, both Voyager spacecraft imaged a detached haze layer surrounding Titan, separated from the main haze distribution by a gap at around 300 km and merging into a hood of more concentrated haze at Titan’s north pole. We have processed Hubble Space Telescope images of Titan with Lucy-Richardson and PIXON deconvolution software and point spread functions generated by TinyTim 6...