<title>Image restoration in minimum-redundancy optical arrays</title>

Abstract

The problem of the short-exposure image restoration for post detection turbulence compensation in minimum-redundancy linear optical arrays is considered for general a priori limitation. A decision procedure for solving the problems of this class is proposed that consists in formalizid registering the a priori information, finding a stable (regularized) solution and devising a numerical restoration algorithm, which based on the global optimization methods. It is shown that this optimization procedure can be used for image restoration in arbitrary optical aperture synthesis systems. An example of the undistorted test restoration is given.

<title>Digital adaptation algorithms of adaptive optics corrected images</title>

“…On their basis the concrete algorithms of global optimization are constructed. One of them, based on the application of the best points from ones obtained before, relative to the construction of a single SE image, is considered in [3]. General considerations, put in the basis of this algorithm, are converged to the fact, that it is more advantageous on average to make the next calculations of the functional S near the point, in which the value of So is the least from the others obtained, than far from it.…”

“…Numerical researches of the given algorithm have been done for a test problem, described in [3]. In the limits of this problem, the aperture of linear form was divided by n16 domains, corresponding to the correlation field cells at the aperture, in each domain random phases O={E, i=l.…”

“…As it is seen from these figures, by the reduction of q. distorted images acquire a clearly expressed noise-like structure, and small details begin to vanish in restored images, that is, the resolution is worsened. It takes place by two causes: -firstly, with increase of intensity of additive noises in an initial image in a smoothed component of an estimated signal at the output of Tikhonov's filter (7), the noise component begins to prevail [16]; secondly, under reduction of q, the fluctuative component of phase fluctuation estimation error at the aperture is increased, that is characterized by the offset of a global extremum from the point of a true value of phase fluctuations [3]. Under small S/N ratio q (q1O), the noise component prevails in the distorted image -it is impossible to identify an object by a light spot in the center of a frame.…”

“…A concrete aspect of physical a-priori limitations for the problems of forming and processing of SE optical images is given in the work [3]. It is shown there also, that in the limits of considered optimization approach, the procedure of inverse operator R construction reduces to a variational problem: r i, (4) mmS[10 (r)] = mm I [i; (i)f dF where J (7) -projection of the function J (7) onto the multitude of non-positive functions; H1 -set of a-priori limitations, at which the function I (7) was defined, under the presence of limitations H1 to the class of optical transfer functions (OFT), defined by by the value of an average module square of OTF (i AT 2 ) for the concrete conditions of atmospheric "seeing" .…”

“…One of such approaches is the Zielinski's methodology 110], based on the algorithm for global search "multistart" In the numerical analysis of the multiextreme functional structure, the example was applied, given in [3]. The dimensionality of optimization space in this case was equal n16, and the total number of local optimization cycles N=l28.…”