Maximum A Posterior Research Articles

Integrated joint source-channel symbol-by-symbol decoding of variable-length codes using 3-D MAP sequence estimation

Most of multimedia schemes employ variable-length codes (VLCs) like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder (I-JSCD) at a symbol-level using three-dimensional (3-D) trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional (2-D) state-space, and then develops a 3-D trellis and a maximum a-posterior (MAP) algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of (50%) data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links.

Estimating Optimal Parameters for MRF Stereo from a Single Image Pair

This paper presents a novel approach for estimating the parameters for MRF-based stereo algorithms. This approach is based on a new formulation of stereo as a maximum a posterior (MAP) problem in which both a disparity map and MRF parameters are estimated from the stereo pair itself. We present an iterative algorithm for the MAP estimation that alternates between estimating the parameters while fixing the disparity map and estimating the disparity map while fixing the parameters. The estimated parameters include robust truncation thresholds for both data and neighborhood terms, as well as a regularization weight. The regularization weight can be either a constant for the whole image or spatially-varying, depending on local intensity gradients. In the latter case, the weights for intensity gradients are also estimated. Our approach works as a wrapper for existing stereo algorithms based on graph cuts or belief propagation, automatically tuning their parameters to improve performance without requiring the stereo code to be modified. Experiments demonstrate that our approach moves a baseline belief propagation stereo algorithm up six slots in the Middlebury rankings.

Super-Resolution Reconstruction Based on Generalized Huber-MRF Image Modeling

Super-Resolution (SR) reconstruction has been a very hot research topic currently. A kind of generalized MRF (GMRF, generalized Markov random field) models is firstly proposed based on the recently reported bilateral filtering. The GMRF model is not only edge-preserving and robust to noise, inherited directly from the bilateral filtering, but also connects the bilateral filtering with the Bayesian MAP (maximum a posterior) approaches much concisely. Meanwhile, an improved numerical scheme of anisotropic diffusion PDE's (partial differential equation) is deduced based on the GMRF model. In the MRF-MAP framework, a new SR restoration algorithm is subsequently proposed for both cases of Gaussian noise and impulse noise, utilizing the generalized Huber-MRF model which guarantees strictly global convergence. The half-quadratic regularization approach and steepest descent are exploited to solve the energy functional. Experimental results demonstrate the effectiveness of this approach, both in the visual effect and the PSNR value.

Neural network-based image reconstruction for positron emission tomography

Positron emission tomography (PET) is one of the key molecular imaging modalities in medicine and biology. Penalized iterative image reconstruction algorithms frequently used in PET are based on maximum-likelihood (ML) and maximum a posterior (MAP) estimation techniques. The ML algorithm produces noisy artifacts whereas the MAP algorithm eliminates noisy artifacts by utilizing availableprior information in the reconstruction process. The MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class and irrespective of the strength of interaction between the nearest neighbors. A Hebbian neural learning scheme is proposed to model the nature of interpixel interaction to reconstruct artifact-free edge preserving reconstruction. A key motivation of the proposed approach is to avoid oversmoothing across edges that is often the case with MAP algorithms. It is assumed that local correlation plays a significant role in PET image reconstruction, and proper modeling of correlation weight (which defines the strength of interpixel interaction) is essential to generate artifact-free reconstruction. The Hebbian learning-based approach modifies the interaction weight by adding a small correction that is proportional to the product of the input signal (neighborhood pixels) and output signal. Quantitative analysis shows that the Hebbian learning-based adaptive weight adjustment approach is capable of producing better reconstructed images compared with those reconstructed by conventional ML and MAP-based algorithms in PET image reconstruction.

A primary study on resolution of overlapping GC-MS signal using mean-field approach independent component analysis

Independent component analysis (ICA) has been found to be powerful to separate complex signals. However, chemical signals are generally correlated, instead of independent as hypothesized in ICA. In this study, mean-field independent component analysis (MF-ICA) was investigated to resolve the overlapping gas chromatographic-mass spectrometric (GC-MS) signal. In MF-ICA, the sources are estimated from the mean of their posterior distribution. The mixing matrix and noise level are found through the maximum a posterior (MAP) solution. By simulated signals, results show that for cases of the slightly correlated (or overlapped) sources, both the sources (MS) and mixing matrix (chromatogram) can be almost correctly estimated by specification of the nonnegative (positive) priors for the mixing matrix and sources. However, when the sources are highly correlated, no good results can be obtained, although acceptable estimated sources can be obtained somehow for database matching. For experimental overlapping GC-MS data, reasonable results are obtained, because MS spectra of different homologous compounds in GC-MS analysis of a mixture are not generally correlated very much. Therefore, ICA should be an alternate tool for resolution of overlapping chemical signals, although further works are still needed.

Steerable pyramid-based face hallucination

In this paper we propose a robust learning-based face hallucination algorithm, which predicts a high-resolution face image from an input low-resolution image. It can be utilized for many computer vision tasks, such as face recognition and face tracking. With the help of a database of other high-resolution face images, we use a steerable pyramid to extract multi-orientation and multi-scale information of local low-level facial features both from the input low-resolution face image and other high-resolution ones, and use a pyramid-like parent structure and local best match approach to estimate the best prior; then, this prior is incorporated into a Bayesian maximum a posterior (MAP) framework, and finally the high-resolution version is optimized by a steepest decent algorithm. The experimental results show that we can enhance a 24 × 32 face image into a 96 × 128 one while the visual effect is relatively good.

MRI volumetric analysis of multiple sclerosis: methodology and validation

We present an automatic mixture-based algorithm for segmentation of brain tissues (white and gray matters-WM and GM), cerebral spinal fluid (CSF), and brain lesions to quantitatively analyze multiple sclerosis. The method performs intensity-based tissue classification using multispectral magnetic resonance (MR) images based on a stochastic model. With the existence of white Gaussian noise and spatially invariant blurring in acquired MR images, a Karhunen-Loeve (K-L) domain Wiener filter is applied for accurate noise reduction and resolution restoration on blurred and noisy images to minimize the partial volume effect (PVE), which is a major limiting factor for the quantitative analysis. Following that, we utilize a Markov random field Gibbs model to integrate the local spatial information into the well-established expectation-maximization model-fitting algorithm. Each voxel is then classified by a maximum a posterior (MAP) criterion, indicating its probabilities of belonging to each class, i.e., each voxel is labeled as a mixel with different tissue percentages, leading to further minimization of the PVE. The volumes of WM, GM, CSF, and brain lesions are extracted from the mixture-based segmentation and the corresponding brain atrophies are computed. In this study, we have investigated the accuracy and repeatability of the algorithm with inclusion of noise analysis and point spread function for image resolution enhancement. Experimental results on phantom, healthy volunteer, and patient studies are presented.

Naive Mean Field Approximation for Image Restoration

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which is equivalent to a finite-temperature decoding method. Since a lot of computational time is needed for the MPM estimate to calculate the thermal averages, the mean field method, which is a deterministic algorithm, is often utilized to avoid this difficulty. We present a statistical-mechanical analysis of naive mean field approximation in the framework of image restoration. We compare our theoretical results with those of computer simulation, and investigate the potential of naive mean field approximation.

A multiparametric and multiresolution segmentation algorithm of 3-D ultrasonic data.

An algorithm devoted to the segmentation of 3-D ultrasonic data is proposed. The algorithm involves 3-D adaptive clustering based on multiparametric information: the gray-scale intensity of the echographic data, 3-D texture features calculated from the envelope data, and 3-D tissue characterization information calculated from the local frequency spectra of the radio-frequency signals. The segmentation problem is formulated as a Maximum A posterior (MAP) estimation problem. A multi-resolution implementation of the algorithm is proposed. The approach is tested on simulated data and on in vivo echocardiographic 3-D data. The results presented in the paper illustrate the robustness and the accuracy of the proposed approach for the segmentation of ultrasonic data.

Segmentation of textured images using a multiresolution Gaussian autoregressive model

We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.

Minimum-Description-Length Criterion for Image Interpretation and Data Analysis in Spatial Informatics

Abstract Spatial Informatics typically involves interpretation of remotely sensed images and analysis of multi-sources of data. Random perturbation in the observations and diversity of hypothesized models give rise to the uncertainty and difficulty of image interpretation and data analysis. The Minimum-Description-Length (MDL) principle is a beet established criterion, which selects the best model with the minimal length of jointly encoding the data and the model. Although in terms of probability, MDL criterion is equivalent to the Maximum Aposterior Probability (MAP) criterion, it is advantageous at Combining different data types and different model structures in a uniform measure – the total number of bits. It is more realistic to computerized information processing, because everything is discrete with limited resolution. This paper clarifies the formulation of the MDL criterion, its relationships to information theory, stochastic complexity, and Bayesian decision strategy. To sufficiently demonstrate t...

A generalized Gaussian image model for edge-preserving MAP estimation

The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.

Bayesian estimation in seismic migration

Seismic migration is a technique widely used in seismic oil exploration for wavefield reconstruction and for imaging the geometrical distribution of the reflection surfaces within the Earth from the seismic data recorded on the Earth surface. These data are usually corrupted by noise (white noise, surface waves, multiple reflections, etc.) that degrades the result of the migration. Another factor which influences the migration is the inadequate knowledge of the distribution of the acoustic wave propagation velocity in the subsurface of the Earth. The authors use estimation theory techniques to find the MAP (maximum a posterior) estimate of the wave propagation velocity and the geometrical distribution of the subsurface reflector points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Digital Phase Lock for Optimum Demodulation

This paper considers the discrete-time demodulation of random angle modulated signals embedded in Gaussian noise. It is first shown, with the aid of the discrete Karhunen-Loeve expansion, that under suitable conditions, a particular nonuniform sampling digital phase lock loop (DPLL) is the approximately optimum digital al demodulator in the maximum a posterior (MAP) sense. significance is the fact that the phase detector of this digital loop consists merely of a sampler; a digital multiplier is not required at the loop input. Next, an approximate nonlinear analysis is carried out for the condition in which random phase modulation is present at the input of a first order loop of the above class. These results are confirmed by simulation. Finally, the optimum demodulators for phase and frequency modulation are derived via Kalman filtering techniques and their performances presented.