Blind deconvolution by simulated annealing

A technique for deconvolving an image from both a single convolution and an ensemble of differently blurred images is presented. The method is more robust than the earlier blind deconvolution algorithms proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and Davey et al. [ Opt. Commun.69, 353 ( 1989)]. The performance of the algorithm in the presence of noise is evaluated. It is also demonstrated how the algorithm can be modified to utilize the much greater amount of information contained in an ensemble of differently blurred pictures of an image. Reconstructions using both computer simulations and infrared astronomical speckle data are presented. The speckle reconstructions are compared with those obtained by both Fourier phase retrieval and bispectral estimation.

Blind deconvolution of speckle images

Blind deconvolution seeks to deblur an image without knowing the cause of the blur. Iterative methods are commonly applied to that problem, but the iterative process is slow, uncertain, and often ill-behaved. This paper considers a significant but limited class of blurs that can be expressed as convolutions of two-dimensional symmetric Levy "stable" probability density functions. This class includes and generalizes Gaussian and Lorentzian distributions. For such blurs, methods are developed that can detect the point spread function from one-dimensional Fourier analysis of the blurred image. A separate image deblurring technique uses this detected point spread function to deblur the image. Each of these two steps uses direct noniterative methods and requires interactive tuning of parameters. As a result, blind deblurring of 512 × 512 images can be accomplished in minutes of CPU time on current desktop workstations. Numerous blind experiments on synthetic data show that for a given blurred image, several di...

Direct blind deconvolution

We report computer observations on the performance of an improved version of a simulated-annealing algorithm that was used before for the problem of phase retrieval. According to the results, we propose to use this method in conjunction with the algorithm of Fienup [ Opt. Lett.3, 27 ( 1978);Opt. Eng.18529, ( 1979);Appl. Opt.21, 2758 ( 1982). The full power of the simulated-annealing algorithm with large arrays appears to be limited by present-day computers rather than by its numerical performance, but we believe that this combination may constitute an efficient method for phase retrieval.

http://digital.csic.es/bitstream/10261/29987/1/EEA480F9-DF06-B0BA-765B435220E529DD_2997.pdf

Performance of a simulated-annealing algorithm for phase retrieval

The wave aberration of human eyes is retrieved from actual point-spread-function (PSF) data and the modulus of the pupil function. The PSF had been obtained previously by application of a hybrid optical–digital method developed recently. The retrieval is done by using a bidimensional Gerchberg–Saxton phase-retrieval algorithm joined to an iterative phase-unwrapping algorithm. To obtain an adequate convergence, the initial wave aberration for starting the retrieval–unwrapping algorithm is estimated with a nonlinear least-squares algorithm. The resulting wave aberrations for several subjects show irregular aberrations superimposed upon the regular wave-aberration components, with astigmatism being the most important asymmetric aberration.

http://digital.csic.es/bitstream/10261/62054/1/Artal%2c.pdf

Retrieval of wave aberration of human eyes from actual point-spread-function data.

The efficiency of an important class of Newton methods (the Levenberg-Marquardt algorithm) for solving overdetermined sets of nonlinear equations is tested in finding the solution to the two-dimensional phase problem. It is seen that the nonlinearity and number of local minima of the cost function increases dramatically with the size of the object array, making these methods of little practical use for sizes greater than 6 2 6.

M. Nieto-Vesperinas

Papers

A Study of the Performance of Nonlinear Least-square Optimization Methods in the Problem of Phase Retrieval