Identification and Restoration for Blurred Images Based on Markov Random Fields

This paper presents an optimal design method by means of mean field annealing (MFA). The mean field theory (MFT) is introduced, and a certain MFA application extension based on Peierls inequality is explained in detail, the critical temperature that is important for classes of problem while applying MFA is discussed. With MFA, the optimal size design of electromagnetic device is carried out. The results are compared with two existing algorithms, the modified simulated annealing (MSA) and one-variable stochastic simulated annealing based MFA (S-MFA), in both operating cost and final quantities. To modify the final results to reach the global optimum, Hooke-Jeeves pattern search method is adopted. Favorable results show the effectiveness of the proposed scheme.

A robust and adaptive algorithm for segmenting a noisy image is presented. The original (or noise-free) images are modeled by an underlying Gibbs random field (GRF) or equivalently by a Markov random field (MRF), and the driving noise is a mixture of an additive independent Gaussian noise and an outlier process. The processes of maximum a posteriori (MAP) segmentation and maximum-likelihood (ML) estimation for the image model parameters are carried out simultaneously. Both procedures, which are based on stochastic relaxation algorithms with a simulated annealing technique, are efficiently implementable on parallel architectures, such as artificial neural networks. Our proposed method is adaptive in that it recursively segments the noise-corrupted images and estimates the model parameters necessary for the segmentation procedure. We should emphasize that the proposed algorithm is robust in eliminating the effect caused by outliers. Finally, a number of computer simulation experiments are given to demonstrate the robustness and effectiveness of the recursive algorithm.

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls's inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the ;weak-membrane' objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms.

This paper presents a new two-step pseudo maximum a posteriori (MAP) segmentation method for the Markov random field (MRF)-modeled image because the exact MAP estimation is hard to implement due to intractable complexity. The expectation maximization (EM) and Markov Chain Monte Carlo (MCMC) methods are adopted to estimate the parameters for the MRF model due to their comparatively good performance. Although the image segmentation algorithms via graph cuts have become very popular nowadays, our proposed algorithm still performs significantly better in automatic identification and segmentation of fuzzy images than them, which is shown by the quantitative results on synthesized images. In practical applications, the proposed two-step pseudo MAP method is superior in segmenting the fuzzy laser images reflected from the weld pool surfaces during the P-GMAW welding process.

Most of the existing video coding algorithms produce highly visible artifacts in the reconstructed images as the bit-rate is lowered. These artifacts are due to the information loss caused by the quantization process. Since these algorithms treat decoding as simply the inverse process of encoding, these artifacts are inevitable. In this paper, we propose an encoder/decoder paradigm in which both the encoder and decoder solve an estimation problem based on the available bitstream and prior knowledge about the source image and video. The proposed technique makes use of a priori information about the original image through a nonstationary Gauss-Markov model. Utilizing this mode, a maximum a posteriori (MAP) estimate is obtained iteratively using mean field annealing. The fidelity to the data is preserved by projecting the image onto a constraint set defined by the quantizer at each iteration. The performance of the proposed algorithm is demonstrated on an H.261-type video codec. It is shown to be effective in improving the reconstructed image quality considerably while reducing the bit-rate.

A smoothing method for minimum phone error linear regression (MPELR) is proposed in this paper. We show that the objective function for minimum phone error (MPE) can be combined with a prior mean distribution. When the prior mean distribution is based on maximum likelihood (ML) estimates, the proposed method is the same as the previous smoothing technique for MPELR. Instead of ML estimates, maximum a posteriori (MAP) parameter estimate is used to define the mode of prior mean distribution to improve the performance of MPELR. Experiments on a large vocabulary speech recognition task show that the proposed method can obtain 8.4% relative reduction in word error rate when the amount of data is limited, while retaining the same asymptotic performance as conventional MPELR. When compared with discriminative maximum a posteriori linear regression (DMAPLR), the proposed method shows improvement except for the case of limited adaptation data for supervised adaptation.

The EM algorithm is a widely used technique for finding maximum likelihood (ML) estimates when the data are not fully observed. Despite its popularity for computing ML estimates in unrestricted problems and the need for simplified computations for problems with equality and inequality restrictions, there have been few applications of the algorithm to restricted ML estimation. The EM algorithm is presented for restricted ML estimation and provides its applications to the probit model under equality and inequality restrictions using two small data sets.

A novel method for obtaining dense displacement fields from a sequence of frames is presented. The algorithm is based on modeling the displacement field as a Markov random field, hence making it possible to use the equivalence of a Markov random field and a Gibbs distribution. The Gibbs distribution is used to define a mean field probability density function, and the displacement field is found using a mean field annealing algorithm. Mean field annealing is a technique which finds the global or near global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented. >

Terrain aided navigation (TAN) is a way to improve underwater vehicle self navigation ability, which is essentially a nonlinear state estimation problem. The iterative Bayesian method based on maximum a posteriori (MAP) estimation has theoretic advantage in solving such problems. But due to the particularities of underwater vehicles, in some cases the long time continual filter is not suitable for underwater vehicles, where MAP estimation degenerates to maximum likelihood (ML) estimation, and continual filter changes to discontinuous positioning. By analyzing the shape of likelihood function, we found that the influence of false peaks in terrain matching will decrease with the increase of measuring beams, which proves the validity of ML estimation as a positioning method. Then a practical method of obtaining the measuring beams is proposed. Simulations validate these conclusions.

Maximum-likelihood (ML), also given its connection to least-squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. In this paper, after a brief review of the theory behind ML and MAP estimators, we compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a three exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, our results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.

Most of the existing video coding algorithms produce highly visible artifacts in the reconstructed images as the bit-rate is lowered. These artifacts are due to the information loss caused by the quantization process. Since these algorithms treat decoding as simply the inverse process of encoding, these artifacts are inevitable. In this paper, we propose an encoder/decoder paradigm in which both the encoder and decoder solve an estimation problem based on the available bitstream and prior knowledge about the source image and video. The proposed technique makes use of a priori information about the original image through a non- stationary Gauss-Markov model. Utilizing this model, a maximum a posteriori estimate is obtained iteratively using mean field annealing. The fidelity to the data is preserved by projecting the image onto a constraint set defined by the quantizer at each iteration. The performance of the proposed algorithm is demonstrated on an H.261-type video codec. It is shown to be effective in improving the reconstructed image quality considerably while reducing the bit-rate.

Finite mixtures of multivariate skew t (MST) distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour. Recently, they have been exploited as an effective tool for modelling flow cytometric data. A number of algorithms for the computation of the maximum likelihood (ML) estimates for the model parameters of mixtures of MST distributions have been put forward in recent years. These implementations use various characterizations of the MST distribution, which are similar but not identical. While exact implementation of the expectation-maximization (EM) algorithm can be achieved for `restricted' characterizations of the component skew t-distributions, Monte Carlo (MC) methods have been used to fit the `unrestricted' models. In this paper, we review several recent fitting algorithms for finite mixtures of multivariate skew t-distributions, at the same time clarifying some of the connections between the various existing proposals. In particular, recent results have shown that the EM algorithm can be implemented exactly for faster computation of ML estimates for mixtures with unrestricted MST components. The gain in computational time is effected by noting that the semi-infinite integrals on the E-step of the EM algorithm can be put in the form of moments of the truncated multivariate non-central t-distribution, similar to the restricted case, which subsequently can be expressed in terms of the non-truncated form of the central t-distribution function for which fast algorithms are available. We present comparisons to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.

We describe a global optimization method called mean field annealing (MFA) and its application to two basic problems in seismic data processing: Seismic deconvolution and surface related multiple attenuation. MFA replaces the stochastic nature of the simulated annealing method with a set of deterministic update rules that act on the average value of the variables rather than on the variables themselves, based on the mean field approximation. As the temperature is lowered, the MFA rules update the variables in terms of their values at a previous temperature. By minimizing averages, it is possible to converge to an equilibrium state considerably faster than a standard simulated annealing method. The update rules are dependent on the form of the cost function and are obtained easily when the cost function resembles the energy function of a Hopfield network. The mapping of a problem onto a Hopfield network is not a precondition for using MFA, but it makes analytic calculations simpler. The seismic deconvolution problem can be mapped onto a Hopfield network by parameterizing the source and the reflectivity in terms of binary neurons. In this context, the solution of the problem is obtained when the neurons of the network reach their stable states. By minimizing the cost function of the network with MFA and using an appropriate cooling schedule, it is possible to escape local minima. A similar idea can also be applied to design an operator that attenuates surface related multiple reflections from plane‐wave transformed seismograms assuming a 1-D earth. The cost function for the multiple elimination problem is based on the criterion of minimum energy of the multiple suppressed data.

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

This letter presents a precise and rapid clustering method for synthetic aperture radar (SAR) images by embedding a Markov random field (MRF) model in the clustering space and using graph cuts (GCs) to search the optimal clusters for the data. The proposed method is optimal in the sense of maximum a posteriori (MAP). It automatically works in a two-loop way: an outer loop and an inner loop. The outer loop determines the cluster number using a pseudolikelihood information criterion based on MRF modeling, and the inner loop is designed in a ldquohardrdquo membership expectation-maximization (EM) style: in the E step, with fixed parameters, the optimal data clusters are rapidly searched under the criterion of MAP by the GC; and in the M step, the parameters are estimated using current data clusters as ldquohardrdquo membership obtained in the E step. The two steps are iterated until the inner loop converges. Experiments on both simulated and real SAR images test the performance of the algorithm.