Maximum a posteriori estimation

About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.

Row-Column Soft-Decision Feedback Algorithm for Two-Dimensional Intersymbol Interference

Abstract: We present a novel iterative row-column soft decision feedback algorithm (IRCSDFA) for detection of binary images corrupted by 2-D intersymbol interference and additive white Gaussian noise. The algorithm exchanges weighted soft information between row and column maximum a posteriori (MAP) detectors. Each MAP detector exploits soft-decision feedback from previously processed rows or columns. The new algorithm gains about 0.3 dB over the previously best published results for the 2times2 averaging mask. For a non-separable 3times3 mask, the IRCSDFA gains 0.8 dB over a previous soft-input/soft-output iterative algorithm which decomposes the 2-D convolution into 1-D row and column operations.

Statistical maritime radar duct estimation using hybrid genetic algorithm–Markov chain Monte Carlo method

Abstract: [1] This paper addresses the problem of estimating the lower atmospheric refractivity ( M profile) under nonstandard propagation conditions frequently encountered in low-altitude maritime radar applications. This is done by statistically estimating the duct strength (range- and height-dependent atmospheric index of refraction) from the sea surface reflected radar clutter. These environmental statistics can then be used to predict the radar performance. In previous work, genetic algorithms (GA) and Markov chain Monte Carlo (MCMC) samplers were used to calculate the atmospheric refractivity from returned radar clutter. Although GA is fast and estimates the maximum a posteriori ( MAP) solution well, it poorly calculates the multidimensional integrals required to obtain the means, variances, and underlying posterior probability distribution functions of the estimated parameters. More accurate distributions and integral calculations can be obtained using MCMC samplers, such as the Metropolis-Hastings and Gibbs sampling (GS) algorithms. Their drawback is that they require a large number of samples relative to the global optimization techniques such as GA and become impractical with an increasing number of unknowns. A hybrid GA-MCMC method based on the nearest neighborhood algorithm is implemented in this paper. It is an improved GA method which improves integral calculation accuracy through hybridization with a MCMC sampler. Since the number of forward models is determined by GA, it requires fewer forward model samples than a MCMC, enabling inversion of atmospheric models with a larger number of unknowns.

A generalized Gibbs prior for maximum a posteriori reconstruction in SPECT

Abstract: The authors introduce a Gibbs prior for use in MAP (maximum a posteriori) reconstruction in SPECT. This new prior, with three parameters, is able to approximate the results of previously-proposed priors with two parameters, as well as a continuum of others. Also, it allows the user increased flexibility in selecting the properties to be emphasised in the final reconstructed image estimate. The additional flexibility offered by the new prior is important in addressing the problem of selecting a prior and its associated parameters in a clinical situation. The paper demonstrates the importance of the derivative potential function (DPF) of the Gibbs distribution in determining which properties will be emphasized in the iterated image estimates. The effects of each of the three parameters are demonstrated on reconstructions from acquired SPECT data. The authors conclude that the parameters must be chosen carefully with consideration for the object distribution and the relative requirements for low-contrast detail, smoothing and edge sharpness in the reconstructed image.

Expectation consistent approximate inference: Generalizations and convergence

Abstract: Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. The proposed method, called Generalized Expectation Consistency (GEC), can be applied to both maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimation. Here we characterize its fixed points, convergence, and performance relative to the replica prediction of optimality.

A MAP-Based Approach for Hyperspectral Imagery Super-Resolution

Abstract: In this paper, we propose a novel single image Bayesian super-resolution (SR) algorithm where the hyperspectral image (HSI) is the only source of information. The main contribution of the proposed approach is to convert the ill-posed SR reconstruction problem in the spectral domain to a quadratic optimization problem in the abundance map domain. In order to do so, Markov random field based energy minimization approach is proposed and proved that the solution is quadratic. The proposed approach consists of five main steps. First, the number of endmembers in the scene is determined using virtual dimensionality. Second, the endmembers and their low resolution abundance maps are computed using simplex identification via the splitted augmented Lagrangian and fully constrained least squares algorithms. Third, high resolution (HR) abundance maps are obtained using our proposed maximum a posteriori based energy function. This energy function is minimized subject to smoothness, unity, and boundary constraints. Fourth, the HR abundance maps are further enhanced with texture preserving methods. Finally, HR HSI is reconstructed using the extracted endmembers and the enhanced abundance maps. The proposed method is tested on three real HSI data sets; namely the Cave, Harvard, and Hyperspectral Remote Sensing Scenes and compared with state-of-the-art alternative methods using peak signal to noise ratio, structural similarity, spectral angle mapper, and relative dimensionless global error in synthesis metrics. It is shown that the proposed method outperforms the state of the art methods in terms of quality while preserving the spectral consistency.