Maximum A Posteriori Probability Research Articles

Analysis and Design of Three-Stage Concatenated Color-Shift Keying

Visible light communication (VLC) relies on abundant unlicensed bandwidth resources. As an attractive high-data-rate modulation scheme designed for VLC, color shift keying (CSK)-assisted modulation is analyzed. We commence our study from an uncoded $M$ -CSK scheme relying on the joint maximum-likelihood (ML) hard detection (HD) of three colors when communicating over an AWGN channel, where both empirical and analytical results are provided. We invoke extrinsic information transfer (EXIT) charts for designing a Maximum a posteriori probability (MAP)-based soft detection (SD)-aided iterative receiver jointly detecting the three colors. Based on the EXIT characteristics of $M$ -CSK, we design different signal labeling strategies for diverse color constellations and detection schemes, which are capable of achieving a substantially improved bit-error-rate (BER) performance. Thus, given fixed transmission power, a CSK system using our proposed signal labeling is capable of increasing the reliable data transmission distance by about 30%.

Integration of fuzzy Markov random field and local information for separation of moving objects and shadows

Major contribution of this article is to devise an efficient moving cast shadow segmentation technique that separates out the moving objects from their shadows casted on the background. It follows two major steps: background separation and shadow detection. For background separation, initially a background model is built. For a particular pixel location we construct the background model by taking the median of pixel values at the corresponding pixel locations in the temporal direction. To suppress the effects of quick change in illumination, and color frequency variation of texture background, in the proposed scheme we have extracted the RGB color features and ten local features at each pixel location in the considered target image frame and the constructed reference image frame. For background separation, a difference image is generated by considering pixel by pixel absolute difference of the thirteen dimensional target image frame and the constructed background model. This is followed by a spatial MRF constrained fuzzy clustering to find the moving regions in the considered scene. The maximum a’posteriori probability (MAP) estimate of the fuzzy statistic based MRF are obtained by fuzzy clustering. The MAP of the MRF constrained fuzzy clustering provides a binary image, where the moving objects with the moving cast shadow are identified as one group and the background is obtained as another group. To segment the moving object from its shadow we explore a three stage shadow analysis technique. It uses analysis of rg color chrominance property of shadow, local gray level co-occurrence based shadow processing followed by boundary refinement to separate out the regions corresponding to the moving cast shadow and moving objects. Performance of the proposed scheme is tested on several test video sequences. Effectiveness of the proposed scheme is verified by comparing the results obtained with those of some of the state-of-the-art techniques.

Memory-Reduced Maximum A Posteriori Probability Decoding for High-Throughput Parallel Turbo Decoders

Wireless communication standards make use of parallel turbo decoder for higher data rate at the cost of large hardware resources. This paper presents a memory-reduced back-trace technique, which is based on a new method of estimating backward-recursion factors, for the maximum a posteriori probability (MAP) decoding. Mathematical reformulations of branch-metric equations are performed to reduce the memory requirement of branch metrics for each trellis stage. Subsequently, an architecture of MAP decoder and its scheduling based on the proposed back trace as well as branch-metric reformulation are presented in this work. Comparative analysis of bit-error-rate (BER) performances in additive white Gaussian noise channel environment for MAP as well as parallel turbo decoders are carried out. It has shown that a MAP decoder with a code rate of 1/2 and a parallel turbo decoder with a code rate of 1/3 have achieved coding gains of 1.28 dB at a BER of 10$$^{-5}$$-5 and of 0.4 dB at a BER of 10$$^{-4}$$-4, respectively. In order to meet high-data-rate benchmarks of recently deployed wireless communication standards, very large scale integration implementations of parallel turbo decoder with 8---64 MAP decoders have been reported. Thereby, savings of hardware resources by such parallel turbo decoders based on the suggested memory-reduced techniques are accounted in terms of complementary metal oxide semiconductor transistor count. It has shown that the parallel turbo decoder with 32 and 64 MAP decoders has shown hardware savings of 34 and 44 % respectively.

A reduced-complexity demapping algorithm for BICM-ID systems

As a highly efficient decoding and demodulation scheme, bit-interleaved coded modulation (BICM) is widely adopted in modern communication systems. In order to enhance the attainable spectral efficiency, usually, high-order modulation schemes are used for BICM systems. When BICM is combined with iterative decoding (BICM-ID), it is capable of further improving the achievable receiver performance. However, the complexity of the standard max-sum approximation of the maximum aposteriori probability in log-domain (Max-Log-MAP) invoked by the iterative demapper is on the order of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> or O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) for a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -ary modulation constellation having m bits per symbol, which may become excessive for high-order BICM-ID systems. The existing simplified algorithms employed for noniterative demappers are based on exploiting the constellation's symmetry, which is no longer retained upon the introduction of the a priori information in BICM-ID systems. Hence, in this paper, a simplified iterative demapping algorithm is proposed to substantially reduce the demapping complexity for a binary-reflected Gray-labeled constellation. Our detailed analysis shows that the simplified demapping scheme proposed for BICM-ID reduces the computational complexity to O(m). We demonstrate that this dramatic computational complexity only imposes modest performance degradation with respect to that of the optimal high-complexity Max-Log-MAP scheme.

Searching Multiregression Dynamic Models of Resting-State fMRI Networks Using Integer Programming

A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents various dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian Networks, the hypothesised relationships accommodate conditional conjugate inference. We demonstrate for the first time how straightforward it is to search over all possible connectivity networks with dynamically changing intensity of transmission to find the Maximum a Posteriori Probability (MAP) model within this class. This search method is made feasible by using a novel application of an Integer Programming algorithm. The efficacy of applying this particular class of dynamic models to this domain is shown and more specifically the computational efficiency of a corresponding search of 11-node Directed Acyclic Graph (DAG) model space. We proceed to show how diagnostic methods, analogous to those defined for static Bayesian Networks, can be used to suggest embellishment of the model class to extend the process of model selection. All methods are illustrated using simulated and real resting-state functional Magnetic Resonance Imaging (fMRI) data.

A blind detection scheme based on modified wavelet denoising algorithm for wireless optical communications

This paper investigates a detection scheme without channel state information for wireless optical communication (WOC) systems in turbulence induced fading channel. The proposed scheme can effectively diminish the additive noise caused by background radiation and photodetector, as well as the intensity scintillation caused by turbulence. The additive noise can be mitigated significantly using the modified wavelet threshold denoising algorithm, and then, the intensity scintillation can be attenuated by exploiting the temporal correlation of the WOC channel. Moreover, to improve the performance beyond that of the maximum likelihood decision, the maximum a posteriori probability (MAP) criterion is considered. Compared with conventional blind detection algorithm, simulation results show that the proposed detection scheme can improve the signal-to-noise ratio (SNR) performance about 4.38dB while the bit error rate and scintillation index (SI) are 1×10−6 and 0.02, respectively.

Normal Inverse Gaussian Model-Based Image Denoising in the NSCT Domain

The objective of image denoising is to retain useful details while removing as much noise as possible to recover an original image from its noisy version. This paper proposes a novel normal inverse Gaussian (NIG) model-based method that uses a Bayesian estimator to carry out image denoising in the nonsubsampled contourlet transform (NSCT) domain. In the proposed method, the NIG model is first used to describe the distributions of the image transform coefficients of each subband in the NSCT domain. Then, the corresponding threshold function is derived from the model using Bayesian maximuma posterioriprobability estimation theory. Finally, optimal linear interpolation thresholding algorithm (OLI-Shrink) is employed to guarantee a gentler thresholding effect. The results of comparative experiments conducted indicate that the denoising performance of our proposed method in terms of peak signal-to-noise ratio is superior to that of several state-of-the-art methods, including BLS-GSM, K-SVD, BivShrink, and BM3D. Further, the proposed method achieves structural similarity (SSIM) index values that are comparable to those of the block-matching 3D transformation (BM3D) method.

Localization of specific language pathways using diffusion-weighted imaging tractography for presurgical planning of children with intractable epilepsy.

To examine whether diffusion-weighted imaging (DWI) tractography can detect multiple white matter pathways connected to language cortices, we employed a maximum a posteriori probability (MAP) classification method, which has been recently validated for the corticospinal tract. DWI was performed in 12 normally developing children and 17 children with intractable focal epilepsy who underwent subsequent two-stage epilepsy surgery with intracranial functional mapping. First, whole-brain DWI tractography was performed to identify unique pathways originating from Broca's area, premotor area, and Wernicke's area on functional magnetic resonance imaging (fMRI) of normal children and intracranial electrical stimulation mapping (ESM) of children with epilepsy. Group averaging of these pathways based on fMRI was performed to construct the probability maps of language areas in standard MRI space. These maps were finally used to design a DWI-MAP classifier, which can automatically sort individual fibers originating from fMRI language areas as well as ESM language areas. In normally developing children, the DWI-MAP classifier predicted language-activation areas on fMRI with up to 77% accuracy. In children with focal epilepsy, the DWI-MAP classifier also showed high accuracy (up to 82%) for the fibers terminating in proximity to essential language areas determined by ESM. Decreased volumes in DWI-MAP-defined pathways after epilepsy surgery were associated with postoperative language deficits. This study encourages further investigations to determine if DWI-MAP analysis can serve as a noninvasive diagnostic tool during pediatric presurgical planning by estimating not only the location of essential language cortices, but also the underlying fibers connecting these cortical areas.

SIFT flow for large-displacement object tracking.

Traditional tracking methods place an emphasis on how to cope with the variations in target appearance effectively. However, when the motion displacement of the target between image frames becomes larger, these methods may be unstable. This paper presents a novel (to our knowledge) visual object tracking method. In this method, we first introduce scale-invariant feature transform (SIFT) flow into the tracking problem and develop a real-time motion prediction method to capture large displacement between consecutive image frames. Then we use belief propagation (BP) to convert the problem of finding maximum a posteriori probability (MAP) to globally minimizing an energy function to get the best matching pairs of points for producing good candidate regions of the target. And last, the refined point trajectories are obtained according to the bidirectional flow field consistency estimation and covariance region descriptor matching, which can update model states efficiently so as to achieve enhanced robustness for visual tracking. Compared with the state-of-art tracking methods, the experimental results demonstrate that the proposed algorithm shows favorable performance when the object undergoes large motion displacement between image frames.

Application of Gibbs–Markov random field and Hopfield-type neural networks for detecting moving objects from video sequences captured by static camera

In this article, we propose a moving objects detection scheme using Gibbs---Markov random field(GMRF) and Hopfield-type neural network (HTNN) in expectation maximization (EM) framework for video sequences captured by static camera. In the considered technique, the background model is built by considering a running Gaussian average over few past frames. The change vector analysis (CVA) scheme is followed on the considered target frame and the constructed reference frame to generate a difference image. The moving objects in target frame are detected by segmenting the difference image into two classes: changed and unchanged, where the changed class represents moving object regions and the unchanged class the background regions. For segmentation, we have modeled the CVA generated difference image with GMRF and the segmentation problem is solved using the maximum a posteriori probability (MAP) estimation principle. The MAP estimator is found to be exponential in nature; and thus a modified HTNN is exploited for estimating the MAP. The parameters of the GMRF model are estimated using EM algorithm. Experiments are carried out on three video sequences. Results of the proposed change detection scheme are compared with those of the codebook-based background subtraction and GMRF model with graph-cut schemes. It is found that the proposed technique provides better results.

Maximum a Posteriori Probability Estimation for Online Surveillance Video Synopsis

To reduce human efforts in browsing long surveillance videos, synopsis videos are proposed. Traditional synopsis video generation applying optimization on video tubes is very time consuming and infeasible for real-time online generation. This dilemma significantly reduces the feasibility of synopsis video generation in practical situations. To solve this problem, the synopsis video generation problem is formulated as a maximum a posteriori probability (MAP) estimation problem in this paper, where the positions and appearing frames of video objects are chronologically rearranged in real time without the need to know their complete trajectories. Moreover, a synopsis table is employed with MAP estimation to decide the temporal locations of the incoming foreground objects in the synopsis video without needing an optimization procedure. As a result, the computational complexity of the proposed video synopsis generation method can be significantly reduced. Furthermore, as it does not require prescreening the entire video, this approach can be applied on online streaming videos.

Supervised Segmentation of Very High Resolution Images by the Use of Extended Morphological Attribute Profiles and a Sparse Transform

In this letter, a novel supervised segmentation technique based on sparsely representing the stacked extended morphological attribute profiles (EAPs) and maximum a posteriori probability (MAP) is presented for very high resolution (VHR) images. Attribute profiles (APs), which are extracted by using several attributes, are applied to the multispectral VHR image, leading to a set of extended EAPs. Using the sparse prior of representing the pixel with all training samples, the extended multi-AP (EMAP) feature stacked by the EAP features is transformed into a class-dependent residual feature, which can be normalized as a posterior probability distribution of the pixel. A graph-cut approach is utilized to segment the image scene and obtain the final classification result. Experiments were conducted on IKONOS and WorldView-2 data sets. Compared with SVM, object-oriented SVM with majority voting, and some other state-of-the-art methods, the proposed method shows stable and effective results.

Studying effective brain connectivity using multiregression dynamic models

A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents multiple dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian Networks, the hypothesised relationships accommodate conditional conjugate inference. We demonstrate for the first time how it is straightforward to search over all possible connectivity networks with dynamically changing intensity of transmission to find the Maximum a Posteriori Probability (MAP) model within this class. This search method is made feasible by using a novel application of the integer programming algorithm. The search over all possible directed (acyclic or cyclic) graphical structures can be made especially fast by utilising the fact that, within this class of models, the joint likelihood factorizes. We proceed to show how diagnostic methods, analogous to those defined for static Bayesian Networks, can be used to suggest embellishment of the model class to extend the process of model selection. A typical goal of experimental neuroscience is to draw conclusions regarding the causal mechanisms that underpin neural communication. Often the main focus of interest in these experiments includes not only a search for the likely model of a specific individual, but an analysis of shared between-subject e↵ects. Currently, such features are analysed using rather coarse aggregation methods over shared time series. However, here we demonstrate that, using the estimation of multiple causal graphical models and Bayesian hyperclustering techniques, it is possible to use the full machinery of Bayesian methods to formally make inferences in a coherent way which contemplates hypotheses about shared dependences between such populations of subjects. Methods developed here are illustrated using simulated and real resting-state and steady-state task functional Magnetic Resonance Imaging (fMRI) data.

Multiple component codes based generalized LDPC codes for high-speed optical transport.

A class of generalized low-density parity-check (GLDPC) codes suitable for optical communications is proposed, which consists of multiple local codes. It is shown that Hamming, BCH, and Reed-Muller codes can be used as local codes, and that the maximum a posteriori probability (MAP) decoding of these local codes by Ashikhmin-Lytsin algorithm is feasible in terms of complexity and performance. We demonstrate that record coding gains can be obtained from properly designed GLDPC codes, derived from multiple component codes. We then show that several recently proposed classes of LDPC codes such as convolutional and spatially-coupled codes can be described using the concept of GLDPC coding, which indicates that the GLDPC coding can be used as a unified platform for advanced FEC enabling ultra-high speed optical transport. The proposed class of GLDPC codes is also suitable for code-rate adaption, to adjust the error correction strength depending on the optical channel conditions.

A Data-Driven Stochastic Approach for Unmixing Hyperspectral Imagery

In this paper, we propose a two-step Bayesian approach to handle the ill-posed nature of the unmixing problem for accurately estimating the abundances. The abundances are dependent on the scene contents and they represent mixing proportions of the endmembers over an area. In this work, a linear mixing model (LMM) is used for the image formation process in order to derive the data term. In the first step, a Huber-Markov random field (HMRF)-based prior distribution is assumed to model the dependencies within the abundances across the spectral space of the data. The threshold used in the HMRF prior is derived from an initial estimate of abundances obtained using the matched filters. This makes the HMRF prior data-driven, i.e., dHMRF. Final abundance maps are obtained in the second step within a maximum a posteriori probability (MAP) framework, and the objective function is optimized using the particle swarm optimization (PSO). Theoretical analysis is carried out to show the effectiveness of the proposed method. The approach is evaluated using the synthetic and real AVIRIS Cuprite data. The proposed method has the following advantages. 1) The estimated abundances are resistant to noise since they are based on an initial estimate that has high signal-to-noise ratio (SNR). 2) The variance in the abundance maps is well preserved since the threshold in the dHMRF is derived from the data.

On MAP and MMSE estimators for the co-sparse analysis model

The sparse synthesis model for signals has become very popular in the last decade, leading to improved performance in many signal processing applications. This model assumes that a signal may be described as a linear combination of few columns (atoms) of a given synthesis matrix (dictionary). The Co-Sparse Analysis model is a recently introduced counterpart, whereby signals are assumed to be orthogonal to many rows of a given analysis dictionary. These rows are called the co-support.The Analysis model has already led to a series of contributions that address the pursuit problem: identifying the co-support of a corrupted signal in order to restore it. While all the existing work adopts a deterministic point of view towards the design of such pursuit algorithms, this paper introduces a Bayesian estimation point of view, starting with a random generative model for the co-sparse analysis signals. This is followed by a derivation of Oracle, Minimum-Mean-Squared-Error (MMSE), and Maximum-A-posteriori-Probability (MAP) based estimators. We present a comparison between the deterministic formulations and these estimators, drawing some connections between the two. We develop practical approximations to the MAP and MMSE estimators, and demonstrate the proposed reconstruction algorithms in several synthetic and real image experiments, showing their potential and applicability.

Optimal Detector Randomization in Cognitive Radio Systems in the Presence of Imperfect Sensing Decisions

In this study, optimal detector randomization is developed for secondary users in a cognitive radio system in the presence of imperfect spectrum sensing decisions. It is shown that the minimum average probability of error can be achieved by employing no more than four maximum a-posteriori probability (MAP) detectors at the secondary receiver. Optimal MAP detectors and generic expressions for their average probability of error are derived in the presence of possible sensing errors. Also, sufficient conditions are presented related to improvements due to optimal detector randomization.

Despeckling of medical ultrasound kidney images in the curvelet domain using diffusion filtering and MAP estimation

Speckle remains as a fundamental problem in all coherent imaging modalities such as ultrasound, synthetic aperture radar (SAR) and laser. Presence of speckle gives a granular appearance to the image, hence hinders the details of the underlying object. This paper presents a novel speckle reduction method in the curvelet domain with coefficient modelling and diffusion filtering of the coefficients. An un-decimated Άtrous based curvelet transform of the image is done. A shrinkage function is estimated with the curvelet transformed coefficients using Maximum A posteriori Probability (MAP) technique with the priori distribution assumption as Gaussian. Part of the curvelet coefficients are diffusion filtered using Perona Malik Anisotrpic Diffusion filter (PMAD) and the rest of the coefficients are modelled using the estimated shrinkage function. Proposed algorithm has been tested with the synthetic as well as real time ultrasound kidney images and is found to be effective in removing the speckles. The proposed system is compared with the popular spatial domain filters such as Frost, Kuan and Wiener, also with wavelet and curvelet domain methods. Objective evaluation using peak signal to noise ratio (PSNR), coefficient of correlation (CoC) and structural similarity (SSIM) measures have been done to demonstrate the effectiveness of the proposed system.

Low-Complexity LDPC-Coded USTM Noncohereny MIMO Receivers

This paper proposes a scheme of combining low-density parity check (LDPC) code with unitary space time modulation (USTM) for noncoherent multiple-input-multiple-output (MIMO) transmitter and receiver over Rayleigh block fading and additive white Gaussian noise (AWGN) channel. The main aim is to design the low complexity coded noncoherent MIMO receiver which is completely dependent on the structural feature of unitary space-time matrix without sending the pilot symbol at the transmitter and estimating the channel state information at the receiver. Considering soft information required by belief-propagation (BP) iterative decoder of LDPC code, we deduce a maximum a posteriori probability (MAP) demodulating algorithm using a special USTM based on the sine-cosine function. A novel dual-demodulator is conceived for decreasing the computational complexity of this MAP demodulator. Furthermore, the iterative feedback scheme between MAP demodulator and BP decoder is introduced and its modified parameter scheme is considered for further improving performance of the dual-demodulator. Comparing with uncoded USTM, our LDPC-coded USTM MIMO receiver can obtain about 17 dB coding gain at 10-6 BER.

Hidden Markov Model Classification based on Empirical Frequencies of Observed Symbols

Given a sequence of observations, classification among two known hidden Markov models (HMMs) can be accomplished with a classifier that minimizes the probability of error (i.e., the probability of misclassification) by enforcing the maximum a posteriori probability (MAP) rule. For this MAP classifier, the a priori probability of error (before any observations are made) can be obtained, as a function of the length of the sequence of observations, by summing up the probability of error over all possible observation sequences of the given length, which is a computationally expensive task. In this paper, we obtain an upper bound on the probability of error of the MAP classifier. Our results are based on a suboptimal decision rule that ignores the order with which observations occur and relies solely on the empirical frequencies with which different symbols appear. We describe necessary and sufficient conditions under which this bound on the probability of error decreases exponentially with the length of the observation sequence. Apart from the usefulness of the suboptimal rule in bounding the probability of misclassification, its numerous advantages (such as low computational complexity, reduced storage requirements, and potential applicability to distributed or decentralized decision schemes) could prove a useful alternative to the MAP rule for HMM classification in many applications.