Motion estimation using mean field annealing applied to MRI

In this paper we propose an identification and restoration algorithm for image degraded by noise as well as blurring. In our proposed method, the original images are modeled as Markov Random Fields(MRF) and the blurred image is presented by the gaussian blurred model. To estimate the parameters involved in the image model and to restore the degraded images, we use Generalized Maximum Likelihood(GML) estimation. The GML consists of the two procedures which is a Maximum Likelihood(ML) estimation and a Maximum A Posteriori(MAP) estimation. These procedures are implemented by using the Expectation-Maximization(EM) algorithm and mean field annealing(MFA) based on the mean field theory.

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.

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.

This paper presents some new applications of Mean Field Annealing (MFA). a technique which usually finds global minima in nonconvex optimization problems. to the restoration of nuclear medicine and magnetic resonance images. The image restoration technique presented in this paper preserves the edges while reducing noise. By selection of proper parameters, it can be used for segmentation. Nonuniform temperature anneahg is introduced for the restoration of images with signal dependent noise. guod for 3-D images. By the use of successive over-relaxation (SOR) algorithm in minimization, These MFA image restoration techniques are fast enw& for practical use in processing 3-D images.

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.

Magnetic resonance (MR) tagging has shown great potential for noninvasive measurement of the motion of a beating heart. In MR tagged images, the heart appears with a spatially encoded pattern that moves with the tissue. The position of the tag pattern in each frame of the image sequence can be used to obtain a measurement of the 3-D displacement field of the myocardium. The measurements are sparse, however, and interpolation is required to reconstruct a dense displacement field from which measures of local contractile performance such as strain can be computed. Here, the authors propose a method for estimating a dense displacement field from sparse displacement measurements. Their approach is based on a multidimensional stochastic model for the smoothness and divergence of the displacement field and the Fisher estimation framework. The main feature of this method is that both the displacement field model and the resulting estimate equation are defined only on the irregular domain of the myocardium. The authors' methods are validated on both simulated and in vivo heart data.

Optimization is an important subject in solving scientific and engineering problems. One conventional searching technique for finding the global minimum is to use gradient descent, which finds the direction for the next iteration from the gradient of the objective function. For complicated problems, the gradient descent technique often gets stuck at a local minimum where the objective function has surrounding barriers. In addition, the complexity of most combinatorial optimization problems increases dramatically with the problem size and makes it very difficult to obtain the globally optimal solution in a reasonably computational time. Complicated optimization problems could also be solved by using branch-and-bound searching method [1], or by relaxing some constraints and solving the simplified problems [2]. Several attractive methods have been reported to help the solutions of the optimization problems to escape from local minima [3 4, 5, 6, 7, 8, 9, 10]. Simulated annealing is one of the popular approaches which is widely applicable to the combinatorial optimization problems [3, 4]. Simulated annealing is a generalization of iterative improvement methods in that it accepts, with a non-zero but gradually decreasing probability, deterioration in the cost function of an optimization problem. A solution from simulated annealing is close to the global minimum within a polynomial upper bound for the computational time and is independent of the initial condition. Mean field annealing is a deterministic approximation to simulated annealing [7]. It analytically approximates the relevant Boltzmann distribution and can execute at 50 times faster than simulated annealing for some problems. The quality of the solutions produced by mean field annealing is highly dependent on the choice of the initial temperature, the cooling speed and the final temperature. So far, simulated annealing has been successfully reported in layout generation of VLSI circuits [11, 12], test pattern generation [13], integrated-circuit delay reduction [14], image segmentation [15] and noise filtering in image processing [16].

The Markov random field (MRF) formation allows independence over small pixel neighborhoods suitable for SIMD implementation. The equivalence between the Gibbs distribution over global configurations and MRF allows description of the problem as maximizing a probability or, equivalently, minimizing an energy function (EF). The EF is a convenient device for integrating 'votes' from disparate, preprocessed features--mean intensity, variance, moments, etc. Contributions from each feature are simply weighted and summed. The EF is flexible and can be easily modified to capture a priori beliefs about the distribution of the configuration space, and still remain theoretically sound. A unique formulation of the EF is given. Notably, a deterministic edge finder contributes to the EF. Weights are independently assigned to each feature's report (indicators). Simulated annealing is the theoretical mechanism which guarantees convergence in distribution to a global minimum. Because the number of iterations is an exponential function of time, the authors depart from theory and implement a fast, heuristic 'cooling' schedule. A videotape of results on simulated FLIR imagery demonstrates real-time update over the entire image. Actual convergence is still too slow for real-time use (O(1 min.)), but the quality of results compares favorably with other region labeling schemes.

Reports a new method for optimizing satellite broadcasting schedules based on the Hopfield neural model in combination with the mean field annealing theory. A clamping technique is used with an associative matrix, thus reducing the dimensions of the solution space. A formula for estimating the critical temperature for the mean field annealing procedure is derived, hence enabling the updating of the mean field theory equations to be more economical. Several factors on the numerical implementation of the mean field equations using a straightforward iteration method that may cause divergence are discussed; methods to avoid this kind of divergence are also proposed. Excellent results are consistently found for problems of various sizes.

Hopfield neural networks (HNN) and simulated annealing (SA) are two recent approaches to solving many combinatorial optimization problems. But, the disadvantages of HNN are that it can often converge at local minimum and the quality of solutions depends on the initial state because of sensitivity of parameterization. On the other hand, SA is designed to cope with the problem of convergence to a local minimum. SA, however, requires unacceptably large computing time. So, a new algorithm called mean field annealing (MFA) which can be interpreted as a generalization of HNN, is applied to optimization problems efficiently. In this paper, we propose a new approach based on MFA to solving of the minimization problem. Also we show that our approach can be applied to multi-layer as well as two-layer routing, and optimal solutions can be obtained by properly adjusting the parameter in the given energy function.

An iterative decoding algorithm suit- able for channels with Gibbs distributed noise is pre- sented. In particular, we focus on the channel with 2- dimensional correlated noise represented by a Markov random field(MRF). I. INTRODUCTION Excellent empirical performance of turbo codes and LDPC codes has inspired researchers to investigate decoding algo- rithms not only for memoryless channels, but also for chan- nels with memory. In this paper, we discuss a channel model with Gibbs distributed noise. The Gibbs distribution which is an exponential-type distribution appears in many fields such as statistical physics, image analysis, neural network etc.. In particular, we here focus on the channels with 2-dimensional correlated noise represented by a Markov random field(MRF). It is known that a joint distribution of any MRF is a Gibbs distribution. A channel with 2-dimensional correlated noise is shown in Fig.1. 2-dimensional correlated noise

In this paper, we propose a sequence labeling method by using SVM posterior probabilities with a Markov Random Field (MRF) model for colorectal Narrow Band Imaging (NBI) zoom-videoendoscope. Classifying each frame of a video sequence by SVM classifiers independently leads to an output sequence which is unstable and hard to understand by endoscopists. To make it more stable and readable, we use an MRF model to label the sequence of posterior probabilities. In addition, we introduce class asymmetry for the NBI images in order to keep and enhance frames where there is a possibility that cancers might have been detected. Experimental results with NBI video sequences demonstrate that the proposed MRF model with class asymmetry performs much better than a model without asymmetry.

In this paper, we present a general model for contextual multisource and multitemporal classification of satellite imagery based on the Markov random field (MRF). For many remote sensing applications, the robust interpretation and evaluation of remote sensed images require the use of multiple sources of information available about the scene under consideration. Indeed, data provided by individual sensors is incomplete, inconsistent or imprecise. Additional sources may provide complementary information and the fusion of multisource data can create a more consistent interpretation of the scene in which the associated uncertainty is decreased and the reliability of analysis results is increased. Also, temporal data from a single sensor can be considered as separate information sources. The combination of multitemporal data sets over the same scene enhances information on changes that might have occurred in the area observed over time. From all these available data, our objective is to extract more information and achieve greater accuracy in assigning images to thematic classes. The multisource classification model employs a pixel by pixel classification technique that defines the interaction between the different sensors in terms of a sum of sensor specific energy function allowed by MRF. Each sensor is associated with a sensor specific reliability factor. The multitemporal classification model requires the integration into the classification process of the temporal information expressed in terms of transition probabilities from one class at time t-1 to another class at time t according to MRF. The contextual classification model deals with the problem of incorporating into the classification process the contextual information expressed in terms of the spatial interaction that exists between one pixel and pixels in the rest of the scene. This interaction is well modelled by MRF via the Gibbs distribution and Potts model. The general model is tested on three data sets for an urban region of Algiers city. The sets of data are multitemporal LANDSAT TM images acquired during 1985, 1991 and 1996. These sets are both considered as multispectral and multitemporal data. The classification performance is studied in terms of the effect of using remote sensing data from different sensors (respectively of including temporal aspects of data) on the punctual and contextual classification process.

Non-additive image steganographic framework based on variational inference in Markov Random Fields

Ultrasound perfusion imaging is a rapid and inexpensive technique which enables observation of a dynamic process with high temporal resolution. The image acquisition is disturbed by various motion influences due to the acquisition procedure and patient motion. To extract valid information about perfusion for quantification and diagnostic purposes this influence must be compensated. In this work an approach to account for non-linear motion using a markov random field (MRF) based optimization scheme for registration is presented. Optimal transformation parameters are found all at once in a single optimization framework. Spatial and temporal constraints ensure continuity of a displacement field which is used for image transformation. Simulated datasets with known transformation fields are used to evaluate the presented method and demonstrate the potential of the system. Experiments with patient datasets show that superior results could be achieved compared to a pairwise image registration approach. Furthermore, it is shown that the method is suited to include prior knowledge about the data as the MRF system is able to model dependencies between the parameters of the optimization process.