Block Sparse Bayesian Learning Framework Research Articles

Correlated Bayesian Co-Training for Virtual Metrology

A rising challenge in manufacturing data analysis is training robust regression models using limited labeled data. In this work, we investigate a semi-supervised regression scenario, where a manufacturing process operates on multiple mutually correlated states. We exploit this inter-state correlation to improve regression accuracy by developing a novel co-training method, namely Correlated Bayesian Co-training (CBCT). CBCT adopts a block Sparse Bayesian Learning framework to enhance multiple individual regression models which share the same support. Additionally, CBCT casts a unified prior distribution on both the coefficient magnitude and the inter-state correlation. The model parameters are estimated using maximum-a-posteriori estimation (MAP), while hyper-parameters are estimated using the expectation-maximization (EM) algorithm. Experimental results from two industrial examples shows that CBCT successfully leverages inter-state correlation to reduce the modeling error by up to 79.40%, compared to other conventional approaches. This suggests that CBCT is of great value to multi-state manufacturing applications.

Broadband Off-Grid DOA Estimation Using Block Sparse Bayesian Learning for Nonuniform Noise Variance

In this article, an extended block sparse Bayesian learning (SBL) is applied to a linear system for estimating the direction of arrival (DOA). DOA estimation using conventional SBL deteriorates when inconsistent noise occurs (e.g., some sensors in the array are malfunctioning). The SBL is extended to accommodate the nonuniform noise variance and shows superior robustness in DOA estimation owing to its selective usage of sensors under normal conditions. Furthermore, a block SBL framework is adopted to exploit the commonality of DOAs over broadband signal frequency components and their correlation at the array. The transformation matrix in the linear system is composed of replicas for preset arrival angles as its basis. Practically, the DOAs deviate from the on-grid angles in the matrix, which results in degradation by basis mismatch. An off-grid SBL incorporating an inconsistent noise variance and block sparsity is formulated to estimate the DOAs reliably. The extended SBL is applied to simulated and measured data (SWellEx-96), and its results are compared with those from conventional approaches. It exhibits better performance in terms of resolution and denoising. In particular, when a part of the array is malfunctioning, the extended SBL can still estimate the DOAs clearly, whereas other approaches fail.

BSBL-Based DOA and Polarization Estimation with Linear Spatially Separated Polarization Sensitive Array

The problem of multiple incident signals’ direction of arrival (DOA) and polarization estimation with linear spatially separated polarization sensitive array (SS-PSA) is investigated in sparse Bayesian learning (SBL) framework. SS-PSA is widely studied due to its low mutual coupling compared with the spatially collocated polarization sensitive array. On the one hand, the sparse representation of data model of proposed array can be expressed skillfully as a block-sparse representation. On the other hand, block sparse Bayesian learning (BSBL) algorithm has excellent performance in recovering the block-sparse signals. Therefore, in this paper, BSBL algorithm is extended to SS-PSA for DOA and polarization estimation. Firstly, a sparse representation model without parameters coupling is established, where the sparse coefficient vector is a block-sparse signal. Secondly, the expectation–maximization method in BSBL framework, i.e., BSBL-EM algorithm, is proposed to recover the block-sparse signal. Lastly, angles estimation can be obtained from the recovered sparse signal according to the intra-block correlation. Simulation results demonstrate that the BSBL-EM algorithm used in DOA and polarization estimation with SS-PSA exhibits better performance compared with Block Orthogonal Matching Pursuit algorithm and Group Basis Pursuit.

Narrowband Interference Separation for Synthetic Aperture Radar via Sensing Matrix Optimization-Based Block Sparse Bayesian Learning

High-resolution synthetic aperture radar (SAR) operating with a large bandwidth is subject to impacts from various kinds of narrowband interference (NBI) in complex electromagnetic environments. Recently, many radio frequency interference (RFI) suppression approaches for SAR based on sparse recovery have been proposed and demonstrated to outperform traditional ones in preserving the signal of interest (SOI) while suppressing the interference by exploiting their intrinsic structures. In particular, the joint recovery strategy of SOI and NBI with a cascaded dictionary, which eliminates the steps of NBI reconstruction and time-domain cancellation, can further reduce unnecessary system complexity. However, these sparsity-based approaches hardly work effectively for signals from an extended target or NBI with a certain bandwidth, since neither of them is sparse in a prescient domain. Moreover, sub-dictionaries corresponding to different components in the cascaded matrix are not strictly independent, which severely limits the performance of separated reconstruction. In this paper, we present an enhanced NBI separation algorithm for SAR via sensing matrix optimization-based block sparse Bayesian learning (SMO-BSBL) to solve these problems above. First, we extend the block sparse Bayesian learning framework to a complex-valued domain for the convenience of radar signal processing with lower computation complexity and modify it to deal with the separation problem of NBI in the contaminated echo. For the sake of improving the separated reconstruction performance, we propose a new block coherence measure by defining the external and internal block structure, which is used for optimizing the observation matrix. The optimized observation matrix is then employed to reconstruct SOI and NBI simultaneously under the modified BSBL framework, given a known and fixed cascaded dictionary. Numerical simulation experiments and comparison results demonstrate that the proposed SMO-BSBL is effective and superior to other advanced algorithms in NBI suppression for SAR.

NBI mitigation in DSSS communications via block sparse Bayesian learning

Abstract Narrowband interference (NBI) is a common interference pattern in direct-sequence spread-spectrum (DSSS) communications. NBI mitigation is a very important issue to ensure the effectiveness of DSSS communications. However, the existing NBI-mitigation algorithms for DSSS communications are confined to a high sampling rate. In order to solve this problem, compressive sensing (CS) is applied to NBI mitigation in DSSS communications, the impact of NBI on the reconstruction of the DSSS signal after compressed sampling is analyzed, and a newly emerged sparse approximation technique, block sparse Bayesian learning (BSBL), is utilized to estimate NBI in DSSS communications. An NBI-mitigation method in DSSS communications based on BSBL is proposed that uses the BSBL framework algorithm to reconstruct the NBI from the compressed signal and then cancels the interference in the time domain. After the NBI mitigation, the conventional CS algorithm is used to demodulate the DSSS signal in the compressed domain. In order to further improve the performance of the method, a filtering BSBL (FBSBL) framework is proposed using the block-sparsity feature of NBI and noise-like feature of the DSSS signal in the frequency domain. A DSSS communications NBI mitigation algorithm based on FBSBL_EM is designed. An equivalent measurement matrix is constructed use the constructed filtering matrix, which could reduce the noise and DSSS signal components in the procedure of compressed sampling. This leads to a highly accurate NBI reconstruction and further improves the NBI mitigation performance. The reported simulation results demonstrate that the proposed method is effective in cancelling the NBI in DSSS communications and significantly outperforms other conventional methods. A comprehensive analysis and comparison of the algorithm is presented and discussed. The results obtained in this study may be extended to other spread-spectrum communication systems, like the code-division multiple-access (CDMA) system.

Microwave Imaging of Nonsparse Domains Using Born Iterative Method With Wavelet Transform and Block Sparse Bayesian Learning

A microwave technique utilizing the combination of wavelet transform, block sparse Bayesian learning (BSBL), and Born iterative method (BIM) is proposed to image nonsparse domains. The wavelet transform is implemented to convert the nonsparse domain into a sparse domain. Then, BSBL framework based on expectation-maximization (EM) algorithm is applied on the BIM model to reconstruct the original profile of the nonsparse domain. The presented imaging results of a nonsparse model indicate that the proposed technique, in comparison with traditional microwave imaging or compressive-sensing (CS) algorithms, achieve very low normalized error rate (NER) at a short computational time using only small number of antennas. The accuracy, robustness, and effectiveness of the proposed method are further assessed by employing it to detect a hemorrhagic brain stroke in a realistic, numerical head model, which is a nonsparse domain. The obtained results indicate the capability for the technique to detect an early stroke in the realistic nonsparse environment of the human head using only six antennas.

An improved IRLS algorithm for sparse recovery with intra-block correlation

Non-convex l2/lq(0<q<1) minimization method can efficiently recover the block-sparse signals whose non-zero coefficients occur in a few blocks. However, in many applications such as face recognition and fetal ECG monitoring, real-world signals also exhibit intra-block correlations aside from standard block-sparsity. In order to recover such signals exactly and robustly, the block sparse Bayesian learning framework is studied in this paper. In contrast to l2/lq norm minimization the proposed method involves a quadratic Mahalanobisdistance measure on the block and a covariance matrix on the intra-block correlation. The improved iteratively reweighted least-squares algorithm for the induced framework is proposed than the recent known for mixed l2/lq optimization. The proposed algorithm is tested and compared with the mixed l2/lq algorithm on a series of signals modeled by autoregressive processes. Numerical results demonstrate the outperformance of the proposed algorithm and meanfulness of the novel strategy, especially in low sample ratio and large unknown noise level.

Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation

We examine the recovery of block sparse signals and extend the recovery framework in two important directions; one by exploiting the signals' intra-block correlation and the other by generalizing the signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, require knowledge of the block structure. Another family, derived from an expanded BSBL framework, are based on a weaker assumption on the block structure, and can be used when the block structure is completely unknown. Using these algorithms, we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation and improve performance.

Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG Via Block Sparse Bayesian Learning

Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning

We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlations and thus their performance degrades significantly with the correlations. In this work, we propose a block sparse Bayesian learning framework which models the temporal correlations. In this framework we derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlations. Furthermore, our algorithms are better at handling highly underdetermined problems and require less row-sparsity on the solution matrix. We also provide analysis of the global and local minima of their cost function, and show that the SBL cost function has the very desirable property that the global minimum is at the sparsest solution to the MMV problem. Extensive experiments also provide some interesting results that motivate future theoretical research on the MMV model.