Bayesian Learning for Joint Sparse OFDM Channel Estimation and Data Detection

The impulse response of a typical wireless multipath channel can be modeled as a tapped delay line filter whose non-zero components are sparse relative to the channel delay spread. In this paper, a novel method of estimating such sparse multipath fading channels for OFDM systems is explored. In particular, Sparse Bayesian Learning (SBL) techniques are applied to jointly estimate the sparse channel and its second order statistics, and a new Bayesian Cramer-Rao bound is derived for the SBL algorithm. Further, in the context of OFDM channel estimation, an enhancement to the SBL algorithm is proposed, which uses an Expectation Maximization (EM) framework to jointly estimate the sparse channel, unknown data symbols and the second order statistics of the channel. The EM-SBL algorithm is able to recover the support as well as the channel taps more efficiently, and/or using fewer pilot symbols, than the SBL algorithm. To further improve the performance of the EM-SBL, a threshold-based pruning of the estimated second order statistics that are input to the algorithm is proposed, and its mean square error and symbol error rate performance is illustrated through Monte-Carlo simulations. Thus, the algorithms proposed in this paper are capable of obtaining efficient sparse channel estimates even in the presence of a small number of pilots.

Joint Approximately Sparse Channel Estimation and Data Detection in OFDM Systems Using Sparse Bayesian Learning

It is well known that the impulse response of a wide-band wireless channel is approximately sparse, in the sense that it has a small number of significant components relative to the channel delay spread. In this paper, we consider the estimation of the unknown channel coefficients and its support in OFDM systems using a sparse Bayesian learning (SBL) framework for exact inference. In a quasi-static, block-fading scenario, we employ the SBL algorithm for channel estimation and propose a joint SBL (J-SBL) and a low-complexity recursive J-SBL algorithm for joint channel estimation and data detection. In a time-varying scenario, we use a first-order autoregressive model for the wireless channel and propose a novel, recursive, low-complexity Kalman filtering-based SBL (KSBL) algorithm for channel estimation. We generalize the KSBL algorithm to obtain the recursive joint KSBL algorithm that performs joint channel estimation and data detection. Our algorithms can efficiently recover a group of approximately sparse vectors even when the measurement matrix is partially unknown due to the presence of unknown data symbols. Moreover, the algorithms can fully exploit the correlation structure in the multiple measurements. Monte Carlo simulations illustrate the efficacy of the proposed techniques in terms of the mean-square error and bit error rate performance.

NESTED SPARSE BAYESIAN LEARNING FOR BLOCK-SPARSE SIGNALS WITH INTRA-BLOCK CORRELATION

In this work, we address the recovery of block sparse vectors with intra-block correlation, i.e., the recovery of vectors in which the correlated nonzero entries are constrained to lie in a few clusters, from noisy underdetermined linear measurements. Among Bayesian sparse recovery techniques, the cluster Sparse Bayesian Learning (SBL) is an efficient tool for block-sparse vector recovery, with intra-block correlation. However, this technique uses a heuristic method to estimate the intra-block correlation. In this paper, we propose the Nested SBL (NSBL) algorithm, which we derive using a novel Bayesian formulation that facilitates the use of the monotonically convergent nested Expectation Maximization (EM) and a Kalman filtering based learning framework. Unlike the cluster-SBL algorithm, this formulation leads to closed-form EMupdates for estimating the correlation coefficient. We demonstrate the efficacy of the proposed NSBL algorithm using Monte Carlo simulations.

Multispectral Bayesian reconstruction technique for real-time two color fluorescence microscopy

We have developed a real-time imaging method for two-color wide-field fluorescence microscopy using a combined approach that integrates multi-spectral imaging and Bayesian image reconstruction technique. To enable simultaneous observation of two dyes (primary and secondary), we exploit their spectral properties that allow parallel recording in both the channels. The key advantage of this technique is the use of a single wavelength of light to excite both the primary dye and the secondary dye. The primary and secondary dyes respectively give rise to fluorescence and bleed-through signal, which after normalization were merged to obtain two-color 3D images. To realize real-time imaging, we employed maximum likelihood (ML) and maximum a posteriori (MAP) techniques on a high-performance computing platform (GPU). The results show two-fold improvement in contrast while the signal-to-background ratio (SBR) is improved by a factor of 4. We report a speed boost of 52 and 350 for 2D and 3D images respectively. Using this system, we have studied the real-time protein aggregation in yeast cells and HeLa cells that exhibits dot-like protein distribution. The proposed technique has the ability to temporally resolve rapidly occurring biological events.

Joint Channel Estimation and Data Detection in MIMO-OFDM Systems: A Sparse Bayesian Learning Approach

The impulse response of wireless channels between the N-t transmit and N-r receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., NtNt the channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster-sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this paper, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the sparse Bayesian learning (SBL) framework and propose a bouquet of novel algorithms for pilot-based channel estimation, and joint channel estimation and data detection, in MIMO-OFDM systems. The proposed algorithms are capable of estimating the sparse wireless channels even when the measurement matrix is only partially known. Further, we employ a first-order autoregressive modeling of the temporal variation of the ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking, and data detection. We also propose novel, parallel-implementation based, low-complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the benefit of exploiting the gac-sparse structure in the wireless channel in terms of the mean square error (MSE) and coded bit error rate (BER) performance.

Bayesian Online Changepoint Detection

Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, most Bayesian papers have focused on the retrospective segmentation problem. Here we examine the case where the model parameters before and after the changepoint are independent and we derive an online algorithm for exact inference of the most recent changepoint. We compute the probability distribution of the length of the current ``run,'' or time since the last changepoint, using a simple message-passing algorithm. Our implementation is highly modular so that the algorithm may be applied to a variety of types of data. We illustrate this modularity by demonstrating the algorithm on three different real-world data sets.

A Bayesian Approach to the Restoration of Degraded Audio Signals

In this paper we derive the a posteriori probability for the location of bursts of noise additively superimposed on a Gaussian AR process. The theory is developed to give a sequentially based restoration algorithm suitable for real-time applications. The algorithm is particularly appropriate for digital audio restoration, where clicks and scratches may be modelled as additive bursts of noise. Experiments are carried out on both real audio data and synthetic AR processes and Significant improvements are demonstrated over existing restoration techniques. © 1995 IEEE

A Bayesian method for identification of stock mixtures from molecular marker data

Molecular markers have been demonstrated to be useful for the estimation of stock mixture proportions where the origin of individuals is determined from baseline samples. Bayesian statistical methods are widely recognized as providing a preferable strategy for such analyses. In general, Bayesian estimation is based on standard latent class models using data augmentation through Markov chain Monte Carlo techniques. In this study, we introduce a novel approach based on recent developments in the estimation of genetic population structure. Our strategy combines analytical integration with stochastic optimization to identify stock mixtures. An important enhancement over previous methods is the possibility of appropriately handling data where only partial baseline sample information is available. We address the potential use of nonmolecular, auxiliary biological information in our Bayesian model.

Bayesian approach to signal modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probability densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

The Bayesian Approach to Signal Modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probabilitiy densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Bayesian signal processing

The application of Bayes' Theorem to signal processing provides a consistent framework for proceeding from prior knowledge to a posterior inference conditioned on both the prior knowledge and the observed signal data. The first part of the lecture will illustrate how the Bayesian methodology can be applied to a variety of signal processing problems. The second part of the lecture will introduce the concept of Markov Chain Monte-Carlo (MCMC) methods which is an effective approach to overcoming many of the analytical and computational problems inherent in statistical inference. Such techniques are at the centre of the rapidly developing area of Bayesian signal processing which, with the continual increase in available computational power, is likely to provide the underlying framework for most signal processing applications.

Bayesian correlated clustering to integrate multiple datasets.

MOTIVATION: The integration of multiple datasets remains a key challenge in systems biology and genomic medicine. Modern high-throughput technologies generate a broad array of different data types, providing distinct-but often complementary-information. We present a Bayesian method for the unsupervised integrative modelling of multiple datasets, which we refer to as MDI (Multiple Dataset Integration). MDI can integrate information from a wide range of different datasets and data types simultaneously (including the ability to model time series data explicitly using Gaussian processes). Each dataset is modelled using a Dirichlet-multinomial allocation (DMA) mixture model, with dependencies between these models captured through parameters that describe the agreement among the datasets. RESULTS: Using a set of six artificially constructed time series datasets, we show that MDI is able to integrate a significant number of datasets simultaneously, and that it successfully captures the underlying structural similarity between the datasets. We also analyse a variety of real Saccharomyces cerevisiae datasets. In the two-dataset case, we show that MDI's performance is comparable with the present state-of-the-art. We then move beyond the capabilities of current approaches and integrate gene expression, chromatin immunoprecipitation-chip and protein-protein interaction data, to identify a set of protein complexes for which genes are co-regulated during the cell cycle. Comparisons to other unsupervised data integration techniques-as well as to non-integrative approaches-demonstrate that MDI is competitive, while also providing information that would be difficult or impossible to extract using other methods.

An example of the use of neural computing techniques in materials science - The modelling of fatigue thresholds in Ni-base superalloys

Two adaptive numerical modelling techniques have been applied to prediction of fatigue thresholds in Ni-base superalloys. A Bayesian neural network and a neurofuzzy network have been compared, both of which have the ability to automatically adjust the network's complexity to the current dataset. In both cases, despite inevitable data restrictions, threshold values have been modelled with some degree of success. However, it is argued in this paper that the neurofuzzy modelling approach offers real benefits over the use of a classical neural network as the mathematical complexity of the relationships can be restricted to allow for the paucity of data, and the linguistic fuzzy rules produced allow assessment of the model without extensive interrogation and examination using a hypothetical dataset. The additive neurofuzzy network structure means that redundant inputs can be excluded from the model and simple sub-networks produced which represent global output trends. Both of these aspects are important for final verification and validation of the information extracted from the numerical data. In some situations neurofuzzy networks may require less data to produce a stable solution, and may be easier to verify in the light of existing physical understanding because of the production of transparent linguistic rules. © 1999 Elsevier Science S.A.

Using ant colony optimisation in learning Bayesian network equivalence classes

R. Daly, Q. Shen and S. Aitken. Using ant colony optimisation in learning Bayesian network equivalence classes. Proceedings of the 2006 UK Workshop on Computational Intelligence, pages 111-118.

Compositional Bayesian modelling and its application to decision support in crime investigation

J. Keppens, Q. Shen and M. Lee. Compositional Bayesian modelling and its application to decision support in crime investigation. Proceedings of the 19th International Workshop on Qualitative Reasoning, pages 138-148.