Statistic-based MAP image-reconstruction from Poisson data usingGibbs priors

A statistical method for selecting the Gibbs parameter in MAP image restoration from Poisson data using Gibbs priors is presented. The Gibbs parameter determines the degree to which the prior influences the restoration. The presented method yields a MAP restored image, minimally influenced by the prior, for which a statistic falls within an appropriate confidence interval. The method assumes that a close approximation to the blurring function is known. A simple iterative feedback algorithm is presented to statistically select the parameter as the MAP image restoration is being performed. This algorithm is heuristically based on a model reference control formulation, but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value. The performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2-D and 3-D images     

Image despeckling and deblurring via regularized complex diffusion

In this paper an image restoration and enhancement model is being proposed, which is suitable for multiplicative data-dependent speckle noise (whose intensity is Gamma distributed) under linear shift-invariant blurring artifacts. The proposed strategy devises a nonlinear second-order diffusive-reactive model for enhancing and restoring images degraded by the aforementioned scenario. The reactive term is derived based on the Maximum a posteriori (MAP) estimator, to make it adaptive to the noise distribution in the input data. This noise-adaptive reactive term helps to restore and enhance the images under data-correlated noise setup. Unlike the other second-order nonlinear diffusion methods, the proposed solution preserves edges and details and reduces piecewise constant approximation in the homogeneous intensity regions in the course of its evolution. The experimental results demonstrated in this paper duly support the above claims.     

Efficient Huber-Markov edge-preserving image restoration.

The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.     

Expectation-maximization algorithms, null spaces, and MAP imagerestoration

A computationally efficient, easily implementable algorithm for MAP restoration of images degraded by blur and additive correlated Gaussian noise using Gibbs prior density functions is derived. This algorithm is valid for a variety of complete data spaces. The constraints upon the complete data space arising from the Gaussian image formation model are analyzed and a motivation is provided for the choice of the complete data, based upon the ease of computation of the resulting EM algorithms. The overlooked role of the null space of the blur operator in image restoration is introduced. An examination of this role reveals an important drawback to the use of the simulated annealing algorithm in maximizing a specific class of functionals. An alternative iterative method for computing the nullspace component of a vector is given. The ability of a simple Gibbs prior density function to enable partial recovery of the component of an image within the nullspace of the blur operator is demonstrated.     

Parallel algorithms for maximum a posteriori estimation of spin density and spin-spin decay in magnetic resonance imaging

A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gradients are assumed: the y-encode gradient applied during the phase preparation time of duration tau before measurement collection, and the x-encode gradient applied during the full data collection time t>/=0. The MRI signal model developed in M.I. Miller et al., J. Magn. Reson., ser. B (Apr. 1995) is used in which a signal resulting from M phase encodes (rows) and N frequency encode dimensions (columns) is modeled as a superposition of MN sinc-modulated exponentially decaying sinusoids with unknown spin-density and spin-spin decay parameters. The nonlinear least-squares MAP estimate of the spin density and spin-spin decay distributions solves for the 2MN spin-density and decay parameters minimizing the squared-error between the measured data and the sine-modulated exponentially decay signal model using an iterative expectation-maximization algorithm. A covariance diagonalizing transformation is derived which decouples the joint estimation of MN sinusoids into M separate N sinusoid optimizations, yielding an order of magnitude speed up in convergence. The MAP solutions are demonstrated to deliver a decrease in standard deviation of image parameter estimates on brain phantom data of greater than a factor of two over Fourier-based estimators of the spin density and spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to separate individual simple minimizations, one for each processor.     

A segmentation-based regularization term for image deconvolution.

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.     

Blood pressure control during surgical operations

In order to reduce intraoperative blood loss and spare blood transfusion, the authors developed a blood pressure control system using a state-predictive controller. Using adult mongrel dogs, the mean arterial pressure (MAP) was recorded from a femoral artery while trimethaphan camsilate was infused at constant rates. A pure delay plus a first-order delay model was then derived from the dose-response curves and the values of plant parameters (gain, time-constant, dead-time, and so on) were estimated based on the experimental data. For this model, a state-predictive servo system was designed to cope with the pure delay existing in the model, and simulated. In order to evaluate the accuracy and reliability of this system, the authors experimented on dogs. with a reference MAP set at 60 mmHg, the MAP reached the reference level in 5.8 to 26.5 min. The duration of error from the reference MAP (±10%) was 2.3±3.9 min/h (n=7). These results indicated the safety and stability of the authors' system     

A multiscale random field model for Bayesian image segmentation

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.     

Improving regulation of mean arterial blood pressure during anesthesia through estimates of surgery effects

In this paper, a scheme for improvement of the regulation of mean arterial blood pressure (MAP) during anesthesia based on model predictive control (MPC) and estimates of the effects of disturbances (surgical events) is proposed. A linear model for the combined effects of surgical stimulations and volatile anesthetics on MAP is derived from experimental data. Based on it the potential improvement in blood pressure regulation is evaluated via a simulation study. The simulation study shows that when information about the effect of the surgical events on MAP is utilized by the controller maximum MAP deviations can be reduced by as much as 50% even when this information is inaccurate. At worst, (highly inaccurate information) no improvement is obtained.     

Restoration of a single superresolution image from several blurred,noisy, and undersampled measured images

The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space- and time-variant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.     

A mobility-based load control scheme in Hierarchical Mobile IPv6 networks

By introducing a mobility anchor point (MAP), Hierarchical Mobile IPv6 (HMIPv6) reduces the signaling overhead and handoff latency associated with Mobile IPv6. In this paper, we propose a mobility-based load control (MLC) scheme, which mitigates the burden of the MAP in fully distributed and adaptive manners. The MLC scheme combines two algorithms: a threshold-based admission control algorithm and a session-to-mobility ratio (SMR)-based replacement algorithm. The threshold-based admission control algorithm gives higher priority to ongoing mobile nodes (MNs) than new MNs, by blocking new MNs when the number of MNs being serviced by the MAP is greater than a predetermined threshold. On the other hand, the SMR-based replacement algorithm achieves efficient MAP load distribution by considering MNs’ traffic and mobility patterns. We analyze the MLC scheme using the continuous time Markov chain in terms of the new MN blocking probability, ongoing MN dropping probability, and binding update cost. Also, the MAP processing latency is evaluated based on the M/G/1 queueing model. Analytical and simulation results demonstrate that the MLC scheme outperforms other schemes and thus it is a viable solution for scalable HMIPv6 networks.     

未知相位信道下 Turbo码编码DPSK信号的联合迭代解调解码

本文提出了未知相位信道下Turbo码编码DPSK信号的联合迭代解调解码算法 .推导了未知相位信道的最大后验概率 (MAP)算法 ,推导表明该MAP算法同样可用前向、后向递推方程来有效实现 .其次 ,采用等效信道的方法将未知相位信道的Turbo码解码问题化为AWGN信道下Turbo码的解码问题 .最后 ,引进了联合迭代解调解码算法 ,可用于Turbo码的解调解码 .模拟表明本文算法可有效用于未知相位信道Turbo码的解码     

Optimal wavelet filter banks for regularized restoration of noisy images

Regularized image restoration methods efficiently handle the ill-posed problem of image restoration. Nevertheless, the issue of selecting the regularization parameter as well as the smoothing filter still constitutes an open research topic. A model of regularized image restoration is introduced and analyzed in this paper. The proposed model assumes that wavelet filter banks replace the smoothing filter of conventional regularized restoration. Filter factorizations for the optimal design of wavelet filter banks using the generalized-cross-validation (GCV) criterion are presented, and novel expressions of the influence matrix, which is used to calculate the GCV error, are derived. The error of the GCV method is expressed in terms of the modulation matrix of the filter bank and the modulation vector of the degradation filter. The expressions are given in general form for optimal wavelet filter bank design upon arbitrary sampling lattices. The numerical examples of image restoration using the proposed method that are presented indicate significant signal-to-noise ratio improvement, _SNR , compared to image restoration methods that employ the Laplacian as the smoothing filter.     

Unifying probabilistic and variational estimation

A maximum a posteriori (MAP) estimator using a Markov or a maximum entropy random field model for a prior distribution may be viewed as a minimizer of a variational problem.Using notions from robust statistics, a variational filter referred to as a Huber gradient descent flow is proposed. It is a result of optimizing a Huber functional subject to some noise constraints and takes a hybrid form of a total variation diffusion for large gradient magnitudes and of a linear diffusion for small gradient magnitudes. Using the gained insight, and as a further extension, we propose an information-theoretic gradient descent flow which is a result of minimizing a functional that is a hybrid between a negentropy variational integral and a total variation. Illustrating examples demonstrate a much improved performance of the approach in the presence of Gaussian and heavy tailed noise. In this article, we present a variational approach to MAP estimation with a more qualitative and tutorial emphasis. The key idea behind this approach is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in MAP estimation. Using tools from robust statistics and information theory, we show that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance.     

SAR image filtering based on the heavy-tailed Rayleigh model.

Synthetic aperture radar (SAR) images are inherently affected by a signal dependent noise known as speckle, which is due to the radar wave coherence. In this paper, we propose a novel adaptive despeckling filter and derive a maximum a posteriori (MAP) estimator for the radar cross section (RCS). We first employ a logarithmic transformation to change the multiplicative speckle into additive noise. We model the RCS using the recently introduced heavy-tailed Rayleigh density function, which was derived based on the assumption that the real and imaginary parts of the received complex signal are best described using the alpha-stable family of distribution. We estimate model parameters from noisy observations by means of second-kind statistics theory, which relies on the Mellin transform. Finally, we compare the proposed algorithm with several classical speckle filters applied on actual SAR images. Experimental results show that the homomorphic MAP filter based on the heavy-tailed Rayleigh prior for the RCS is among the best for speckle removal.     

Satellite image blind restoration based on surface fitting and multivariate model

Owing to the blurring effect from atmosphere and camera system in the satellite imaging, a blind image restoration algorithm is proposed which includes the modulation transfer function （MTF） estimation and the image restoration. In the MTF estimation stage, based on every degradation process of satellite imaging-chain, a combined parametric model of MTF is given and used to fit the surface of normalized logarithmic amplitude spectrum of degraded image. In the image restoration stage, a maximum a posteriori （MAP） based edge-preserving image restoration method is presented which introduces multivariate Laplacian model to characterize the prior distribution of wavelet coefficients of original image. During the image restoration, in order to avoid solving high nonlinear equations, optimization transfer algorithm is adopted to decom- pose the image restoration procedure into two simple steps： Landweber iteration and wavelet thresholding denoising. In the numerical experiment, the satellite image restoration results from SPOT-5 and high resolution camera （HR） of China ＆ Brazil earth resource satellite （CBERS-02B） ane compared, and the proposed algorithm is superior in the image edge preservation and noise inhibition.     

On the smoothness constraint in the intensity-based estimation of the parallax field

In this contribution, the estimation of the parallax field is considered in a mathematical way. First, a mathematical model for the image formation is developed : This model describes how the parallax field influences the left and the right image. Then, we tackle the inverse problem : We calculate the parallax field given the left and the right image. In fact, the problem of estimating the parallax field is mathematically formulated as the maximum a posteriori probability (MAP) estimation of a Gaussian signal given two (noisy) measured signals, i.e. the left and the right image. Estimation problems like this are considered in [2]. We apply that theory to the problem at hand and prove that the MAP estimate for the parallax field minimizes a certain functional. This functional is compared to the functional of the traditional intensity-based method. Both functionals consist of a term associated with the displaced frame difference and a term associated with the smoothness of the parallax field. Our functional differs from the traditional one in the smoothness term. Next, we consider the searching for the minimum of this functional and develop a new iterative procedure to obtain the MAP estimate in a few iterations. Our procedure is quite different from the Gauss-Seidel or Jacobi schemes [3] that are normally used for this purpose. Finally, some results are given to compare the performance of our smoothness constraint to the traditional one.     

A Novel Method to Get Super-Resolution Images from Low-Resolution Compressed Video

1IntroductionSuper-Resolution (SR) is the process of reconstruct-ing a higher resolution i mage from Low-Resolution(LR)input observations .These LRobservations are ac-quired by either multiple sensors or by a single sensori maging the scene over a period of ti me[1]. No matterthe source of observation,the critical requirement forSRis that the observations contain different but relatedviews of the scene .In the field,there are many typicalmethods proposed to address the problem, such as :B…     

Constrained regularized image restoration using projection on a setof regularized solutions

This article addresses a problem of constrained regularized image restoration. A consistent approach to the solution of this problem is based on minimizing the Tikhonov's (1977) regularizing functional subject to a set of constraints. It is demonstrated that a set of regularized solutions resulting from minimization of Tikhonov's functional is closed and convex and a projection operator on this set is derived