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.

A unified framework for MAP estimation in remote sensing image segmentation

Abstract: A complete framework is proposed for applying the maximum a posteriori (MAP) estimation principle in remote sensing image segmentation. The MAP principle provides an estimate for the segmented image by maximizing the posterior probabilities of the classes defined in the image. The posterior probability can be represented as the product of the class conditional probability (CCP) and the class prior probability (CPP). In this paper, novel supervised algorithms for the CCP and the CPP estimations are proposed which are appropriate for remote sensing images where the estimation process might to be done in high-dimensional spaces. For the CCP, a supervised algorithm which uses the support vector machines (SVM) density estimation approach is proposed. This algorithm uses a novel learning procedure, derived from the main field theory, which avoids the (hard) quadratic optimization problem arising from the traditional formulation of the SVM density estimation. For the CPP estimation, Markov random field (MRF) is a common choice which incorporates contextual and geometrical information in the estimation process. Instead of using predefined values for the parameters of the MRF, an analytical algorithm is proposed which automatically identifies the values of the MRF parameters. The proposed framework is built in an iterative setup which refines the estimated image to get the optimum solution. Experiments using both synthetic and real remote sensing data (multispectral and hyperspectral) show the powerful performance of the proposed framework. The results show that the proposed density estimation algorithm outperforms other algorithms for remote sensing data over a wide range of spectral dimensions. The MRF modeling raises the segmentation accuracy by up to 10% in remote sensing images.

Lidar Waveform-Based Analysis of Depth Images Constructed Using Sparse Single-Photon Data

Abstract: This paper presents a new Bayesian model and algorithm used for depth and reflectivity profiling using full waveforms from the time-correlated single-photon counting measurement in the limit of very low photon counts. The proposed model represents each Lidar waveform as a combination of a known impulse response, weighted by the target reflectivity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded through prior distributions that account for the different parameter constraints and their spatial correlation among the image pixels. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target reflectivity, and a second MRF is used to model the distribution of the target depth, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to perform Bayesian inference. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a series of experiments using real data.

Joint source-channel decoding for variable-length encoded data by exact and approximate MAP sequence estimation

Abstract: Joint source-channel decoding based on residual source redundancy is an effective paradigm for error-resilient data compression. While previous work only considered fixed-rate systems, the extension of these techniques for variable-length encoded data was independently proposed by the authors and by Demir and Sayood (see Proc. Data Comp. Conf., Snowbird, UT, p.139-48, 1998). We describe and compare the performance of a computationally complex exact maximum a posteriori (MAP) decoder, its efficient approximation, an alternative approximate decoder, and an improved version of this decoder are suggested. Moreover, we evaluate several source and channel coding configurations. The results show that our approximate MAP technique outperforms other approximate methods and provides substantial error protection to variable-length encoded data.

VLSI architectures for the MAP algorithm

Abstract: This paper presents several techniques for the very large-scale integration (VLSI) implementation of the maximum a posteriori (MAP) algorithm. In general, knowledge about the implementation of the Viterbi (1967) algorithm can be applied to the MAP algorithm. Bounds are derived for the dynamic range of the state metrics which enable the designer to optimize the word length. The computational kernel of the algorithm is the add-MAX* operation, which is the add-compare-select operation of the Viterbi algorithm with an added offset. We show that the critical path of the algorithm can be reduced if the add-MAX* operation is reordered into an offset-add-compare-select operation by adjusting the location of registers. A general scheduling for the MAP algorithm is presented which gives the tradeoffs between computational complexity, latency, and memory size. Some of these architectures eliminate the need for RAM blocks with unusual form factors or can replace the RAM with registers. These architectures are suited to VLSI implementation of turbo decoders.

A parametric scheme for the retrieval of two-dimensional ocean wave spectra from synthetic aperture radar look cross spectra

Abstract: [1] A parametric inversion scheme for the retrieval of two-dimensional (2-D) ocean wave spectra from look cross spectra acquired by spaceborne synthetic aperture radar (SAR) is presented. The scheme uses SAR observations to adjust numerical wave model spectra. The Partition Rescaling and Shift Algorithm (PARSA) is based on a maximum a posteriori approach in which an optimal estimate of a 2-D wave spectrum is calculated given a measured SAR look cross spectrum (SLCS) and additional prior knowledge. The method is based on explicit models for measurement errors as well as on uncertainties in the SAR imaging model and the model wave spectra used as prior information. Parameters of the SAR imaging model are estimated as part of the retrieval. Uncertainties in the prior wave spectrum are expressed in terms of transformation variables, which are defined for each wave system in the spectrum, describing rotations and rescaling of wave numbers and energy as well as changes of directional spreading. Technically, the PARSA wave spectra retrieval is based on the minimization of a cost function. A Levenberg-Marquardt method is used to find a numerical solution. The scheme is tested using both simulated SLCS and ERS-2 SAR data. It is demonstrated that the algorithm makes use of the phase information contained in SLCS, which is of particular importance for multimodal sea states. Statistics are presented for a global data set of 11,000 ERS-2 SAR wave mode SLCS acquired in southern winter 1996.