Restoration, Maximum Entropy Method

Color Science Computer Algorithms Computer Architecture Image-Guided Surgery Image Restoration, Maximum Entropy Methods... 

Aerosols Atmospheric Diffusion Modeling Atmospheric Turbulence Flow Visualization Image Restoration, Maximum Entropy Method Imaging Optics Mesoscale Atmospheric Modeling Radiation, Atmospheric Wave Phenomena... 

The classical computer tomography (CT), including the medical one, has already been demonstrated its efficiency in many practical applications. At the same time, the request of the all-round survey of the object, which is usually unattainable, makes it important to find alternative approaches with less rigid restrictions to the number of projections and accessible views for observation. In the last time, it was understood that one effective way to withstand the extreme lack of data is to introduce a priori knowledge based upon classical inverse theory (including Maximum Entropy Method (MEM)) of the solution of ill-posed problems [1-6]. As shown in [6] for objects with binary structure, the necessary number of projections to get the quality of image restoration compared to that of CT using multistep reconstruction (MSR) method did not exceed seven and eould be reduced even further. 

In the Maximum Entropy Method (MEM) which proceeds the maximization of the conditional probability P(fl p ) (6) yielding the most probable solution, the probability P(p) introducing the a priory knowledge is issued from so called ergodic situations in many applications for image restoration [1]. That means, that the a priori probabilities of all microscopic configurations p are all the same. It yields to the well known form of the functional 5(/2 ) [9] ... 

Like the other nonlinear constrained methods, the maximum-entropy method has proved its capacity to restore the frequency content of 6 that has not survived convolution by s and is entirely absent from the data (Frieden, 1972 Frieden and Burke, 1972). Its importance to the development of deconvolution arises from the statistical concept that it introduced. It was the first of the nonlinear methods explicitly to address the problem of selecting a preferred solution from the multiplicity of possible solutions on the basis of sound statistical arguments. 

The direct demodulation algorithm provides a general approach to handle a large variety of image restoration or reconstruction problems. Computer simulations and analysis results for COS-B and CGRO 7-ray data show that in comparison with traditional techniques, e.g. maximum entropy method, cross-correlation deconvolution or likelihood approach, the direct demodulation method has high sensitivity, high resolution ability and capability to effectively reduce the effect of statistical fluctuations and noise in data and to simultaneously restore both the extended and discrete features in the object. 

The maximum entropy method was one of several techniques that were used to restore the Hubble images. However, all techniques were hampered by lack of complete knowledge of the point-spread function. Using a point-spread function that included errors (either because of noise in a measured point-spread function, or modeling imperfections in predicted point-spread function) further adds to the ill-posed nature of the restoration problem. Although the modulation transfer function tended not to be zero-valued (at least not as severely as in the radio interferometry case described below), this was of only small comfort when imaging weak objects, as the... 

An important issue in the restoration process is photometric linearity—the ability of the restoration technique to maintain a linear relationship between the brightness of a star and the response. Unfortunately, the biases in maximum entropy methods make photometric linearity a difficult proposition. 

Nonlinear approaches to image restoration have proven to be far superior to classical linear approaches. The maximum entropy approach, in particular, has proven to be very flexible in allowing a wide and complex variety of data and constraints to be used in the restoration process. The maximum entropy method, however, is not without... 

Under these prior conditions, the restoring algorithm given by Eqs. (59) and (60) becomes very close to one previously used by Frieden (1972). That one was also a maximum-entropy restoring algorithm in the presence of additive noise. We present some results of the latter method applied to spectral data. 

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