Pattern-Coupled Sparse Bayesian Learning Research Articles

Room Impulse Response Reconstruction Using Pattern-Coupled Sparse Bayesian Learning with Spherical Waves

Room Impulse Response Reconstruction Using Pattern-Coupled Sparse Bayesian Learning with Spherical Waves

High-resolution on-chip spatial heterodyne Fourier transform spectrometer based on artificial neural network and PCSBL reconstruction algorithm.

A novel compact on-chip Fourier transform (FT) spectrometer has been proposed based on the silicon-on-insulator (SOI) platform with wide operating bandwidth and high resolution. The spectrometer consists of a 16-channel power splitter and a Mach-Zehnder interferometer (MZI) array of 16 MZIs with linearly increasing optical path length (OPL) difference. We have also developed a spectral retrieval algorithm based on the pattern-coupled sparse Bayesian learning (PCSBL) algorithm and artificial neural network (ANN). The experimental results show that the designed spectrometer has a flat transmission characteristic in the wavelength range between 1500 nm and 1600 nm, indicating that the device has a wide operating bandwidth of 100 nm. In addition, with the assistance of the spectral retrieval algorithm, our spectrometer has the ability to reconstruct narrowband signals with full width at half maximum (FWHM) of 0.5 nm and a triple-peaked signal separated by a 3-nm distance.

Inverse synthetic aperture radar autofocus imaging of block structure targets with sparse aperture

Inverse synthetic aperture radar (ISAR) autofocus imaging performance is challenged by the residual phase errors that arise from the traditional motion compensation methods with sparse aperture. Moreover, sparse reconstruction algorithms usually ignore the block sparsity in the ISAR image, which cannot recover structured information of the block structure target completely. An imaging method based on joint minimum Tsallis entropy and pattern-coupled sparse Bayesian learning algorithm is proposed to achieve ISAR autofocus imaging of block structure targets with sparse aperture. A pattern-coupled hierarchical complex Gaussian prior is utilized to characterize the correlation among ISAR image pixels in the complex domain. Such a prior model has the potential to encourage block-sparse patterns and achieve ISAR sparse aperture imaging of block structure targets without knowing the block partition prior information. The residual phase errors are estimated based on the minimum Tsallis entropy criterion during the sparse reconstruction of ISAR image to achieve ISAR autofocus imaging, which has the advantage of improving the computational efficiency compared with minimum Shannon entropy criterion. The superiority of the proposed algorithm is verified by the experimental results based on both simulated and measured data.

Generalized Approximate Message Passing Based Bayesian Learning Detectors for Uplink Grant-Free NOMA

The existing sparse Bayesian learning (SBL) and pattern coupled sparse Bayesian learning (PCSBL) multiuser detection (MUD) algorithms for grant-free non-orthogonal multiple access (GF-NOMA) have high computational complexity, i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> , considering mainly the calculation of posterior distribution of the transmitted signals. In this paper, we embed generalized approximate message passing (GAMP) to SBL and PCSBL, and develop two efficient Bayesian learning algorithms for GF-NOMA systems, that is, generalized approximate message passing sparse Bayesian learning (GAMP-SBL) and generalized approximate message passing pattern coupled sparse Bayesian learning (GAMP-PCSBL). It is shown that the Bayesian algorithms can significantly reduce the computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(NK)$</tex-math></inline-formula> . Simulation results show that these two low complexity detectors still have superior recovery performance than the conventional MUD methods, and nearly have the same performance compared with SBL and PCSBL.

A deep iterative neural network for structured compressed sensing based on generalized pattern-coupled sparse Bayesian learning

Over the last few decades, lots of model-driven methods have been developed for model-based compressed sensing (CS), in which the inherent structures of sparse signals are exploited as priors to promote reconstruction accuracy and robustness. Although these methods obtained positive results, there still exist low prior utilizations. The single model-driven fashion is hard to completely express structured priors. Motivated by the recent flourishing studies of deep learning, we combine the model-based framework of the pattern-coupled sparse Bayesian learning (PC-SBL) with data-driven deep learning method to form a double-driven architecture, dubbed as PC-DINN. First, a generalized model of pattern-coupled Bayesian priors is developed to characterize structured properties, in which learnable scale parameters are generated by a heterogeneous process. Second, we unroll the iterative sparse Bayesian learning (SBL) algorithm to form an interpretable deep iterative neural network, and then treat all the learnable scale parameters of the prior model as weights to be learned. To the best of our knowledge, this is the first combination of model-based SBL and data-driven methods for structured CS. Simulation results suggest that for both the structured sparse signals of block sparsity and tree sparsity, the proposed PC-DINN not only achieves favorable reconstruction accuracy but also overcomes the vulnerability of parameter choice in the framework of PC-SBL.

A Computational Efficient 2-D Block-Sparse ISAR Imaging Method Based on PCSBL-GAMP-Net

Sparse aperture inverse synthesis aperture radar (SA-ISAR) imaging is generally solved by compressed sensing (CS) methods or sparse signal recovery (SSR). Many SSR methods focus on the sparsity of radar images only, which achieves unsatisfactory results on structural data. In addition, most of the traditional CS algorithms suffer from a heavy computational burden. In this article, a new deep unfolding network called pattern-coupled sparse Bayesian learning (PCSBL)-generalized approximate message passing (GAMP)-Net is proposed. The proposed network structure can learn the model of block-sparse information from data to reconstruct images of better quality via fewer iteration steps. First, a complex-valued pattern-coupled hierarchical Gaussian prior model is established. Then, the GAMP algorithm is applied for computational Bayesian inference. Based on the previous PCSBL-GAMP framework, the iterative procedure is unrolled to be a deep network structure. A complex-valued backpropagation (BP) algorithm is derived for network training. Experiment results based on simulated and measured data validate the superiority of the proposed method over the traditional PCSBL-GAMP algorithm. Also, the proposed algorithm is ten times faster than the traditional PCSBL-GAMP algorithm.

Pattern Coupled Sparse Bayesian Learning Based on UTAMP for Robust High Resolution ISAR Imaging

Block sparse Bayesian learning (BSBL) has been widely used in inverse synthetic aperture radar (ISAR) imaging, which significantly improves the imaging performance by exploiting the sparse pattern information of ISAR images. However, the conventional Bayesian learning algorithm has high computational complexity, which hinders its applications to real-time processing of radar imaging. The approximate message passing (AMP) can be used to obtain a low complexity implementation of sparse Bayesian learning (SBL). However, AMP suffers from performance losses and even diverges in the case of high-Doppler resolution ISAR imaging where the measurement matrix can be highly correlated. To solve this problem, we propose a fast pattern coupled SBL ISAR imaging algorithm based on approximate message passing with unitary transformation (UTAMP). First, the estimates of the hyperparameters of sparse vector are obtained through UTAMP based SBL, and then nearest neighbor hyperparameters are coupled and updated for next iteration. With low complexity, the proposed algorithm can effectively exploit the sparse pattern information of ISAR images, and exhibits excellent convergence and imaging performance. Both simulation and real data experiments are carried out to verify the effectiveness of the proposed algorithm.

Scene Segmentation of Multi-Band ISAR Fusion Imaging Based on MB-PCSBL

We consider the problem of achieving multi-band inverse synthetic aperture radar (ISAR) fusion imaging of block structure targets with unknown block partition and develop a block-sparse recovering method based on matrix block pattern-coupled sparse Bayesian learning algorithm. Based on the sparse representation of multi-band ISAR fusion imaging model, a pattern-coupled hierarchical Gaussian prior is proposed to characterize the pattern relevance of scattering coefficients. The sparsity of each coefficient is controlled not only by its own hyperparameter, but also by the hyperparameters corresponding to its eight neighboring coefficients in the data matrix. The correlations between the coefficients in rows and columns are determined by different parameters, respectively. The proposed prior model can increase the model flexibility and promote the generation of block structures. Moreover, the whole observation scene is segmented into multiple sub-scenes to reduce the memory storage space and the computational complexity. Parameters and the fusion image result of each sub-scene are derived by the expectation-maximization method. The multi-band ISAR fusion image result of the whole scene is obtained through the stitching of the sub-scenes imaging results. Experimental results demonstrate the effectiveness and superiority of the proposed algorithm.

Multi-Angle SAR Sparse Image Reconstruction With Improved Attributed Scattering Model

The traditional synthetic aperture radar (SAR) sparse imaging methods are based on the point scattering model. However, this model is not suitable for many distributed targets with large variations in scattering characteristics at different angles, i.e., many distributed targets can no longer be considered as a combination of a series of ideal point scatterers under multi-angle observations. To solve this problem, by introducing the improved attributed scattering model into the traditional SAR echo model, we propose our multi-angle sparse image reconstruction method (MASIRM). Through modeling the illuminated scene with point scatterers and line-segment-scatterers, a multi-angle echo model is first presented. By generating an adaptive mixed dictionary and applying the pattern-coupled sparse Bayesian learning, the MASIRM obtains more geometric information of the distributed target with higher quality sparse SAR images. Real data experiments demonstrate that MASIRM performs favorably against traditional imaging methods.

High-resolution ISAR imaging of fast rotating targets based on pattern-coupled Bayesian strategy for multiple measurement vectors

Very high resolution inverse synthetic aperture radar (ISAR) imaging of fast rotating targets is a complicated task. There may be insufficient pulses or may introduce migration through range cells (MTRC) during the coherent processing interval (CPI) when we use the conventional range Doppler (RD) ISAR technique. With compressed sensing (CS) technique, we can achieve the high-resolution ISAR imaging of a target with limited number of pulses. Sparse representation based method can achieve the super resolution ISAR imaging of a target with a short CPI, during which the target rotates only a small angle and the range migration of the scatterers is small. However, traditional CS-based ISAR imaging method generally faced with the problem of basis mismatch, which may degrade the ISAR image. To achieve the high resolution ISAR imaging of fast rotating targets, this paper proposed a pattern-coupled sparse Bayesian learning method for multiple measurement vectors, i.e. the PC-MSBL algorithm. A multi-channel pattern-coupled hierarchical Gaussian prior is proposed to model the pattern dependencies among neighboring range cells and correct the MTRC problem. The expectation-maximization (EM) algorithm is used to infer the maximum a posterior (MAP) estimate of the hyperparameters. Simulation results validate the effectiveness and superiority of the proposed algorithm.

Alternative to Extended Block Sparse Bayesian Learning and Its Relation to Pattern-Coupled Sparse Bayesian Learning

We consider the problem of recovering block sparse signals with unknown block partition and propose a better alternative to the extended block sparse Bayesian learning (EBSBL). The underlying relationship between the proposed method EBSBL and pattern-coupled sparse Bayesian learning (PC-SBL) is explicitly revealed. The proposed method adopts a cluster-structured prior for sparse coefficients, which encourages dependencies among neighboring coefficients by properly manipulating the hyperparameters of the neighborhood. Due to entanglement of the hyperparameters, a joint sparsity assumption is made to yield a suboptimal analytic solution. The alternative algorithm avoids high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and explains the effectiveness of EBSBL. The proposed algorithm also avoids the vulnerability of parameter choice in PC-SBL. Results of comprehensive simulations demonstrate that the proposed algorithm achieves performance that is close to the best performance of PC-SBL. In addition, it outperforms EBSBL and other recently reported algorithms particularly under noisy and low sampling scenarios.

Novel Bayesian Inference Algorithms for Multiuser Detection in M2M Communications

The fifth generation and future wireless networks are expected to support massive machine-to-machine (M2M) communications. Due to the sporadic nature, massive M2M communications can be well supported by low-activity code division multiple access (LA-CDMA). In the literature, maximum a posteriori detector has been proposed to detect the active users in LA-CDMA when the user activity factor is known and small. However, such user activity factor is usually unknown and could be large in practice, which makes the multiuser detection for LA-CDMA a challenging task. In this paper, we first formulate the LA-CDMA uplink using single measurement vector (SMV) model and multiple measurement vector (MMV) model, then, propose novel Bayesian inference algorithms to recover the transmitted signals. For SMV model, we first introduce sparse Bayesian learning (SBL) that exploits the sparsity of the transmitted signals, then, add on the known finite-alphabet constraints and introduce Gaussian mixture model method to recover the transmitted signals. For MMV model, pattern coupled SBL (PCSBL) algorithm is introduced that takes into consideration the neighbor coherence of each device, then the block SBL is introduced through exploiting the row sparsity property and the column coherence of each device. The four Bayesian inference methods make use of various priors and hyperparameters, which can be autonomously learned through the training process via expectation maximization (EM) or variational EM iterative algorithms. Furthermore, the proposed Bayesian methods do not require the knowledge of user activity factor. Simulation results have shown that the proposed Bayesian inference methods outperform the classical algorithms.

Sparse Bayesian learning using correlated hyperparameters for recovery of block sparse signals

Traditional sparse Bayesian learning applies independent hyperparameters to control the sparsity of each coefficient in the sparse signal. For recovery of block-sparse signals with unknown block partitioning structure, pattern coupled sparse Bayesian learning (PCSBL) method considers the sparsity patterns of the neighboring coefficients to be related to each other and uses a predefined parameter to control the relevance between the hyperparameters. However, for most real signals with block sparsity, the degree of relevance between neighboring coefficients is inhomogeneous, and should be data-dependent. This motivates us to modify PCSBL by replacing the single predefined parameter with a set of data-dependent coupling parameters (DDCP) to capture the relevance. In this paper, by performing a linear transformation to the independent hyperparameters, a set of correlated hyperparameters is generated to build the hierarchical Gaussian prior model for recovery of block sparse signals. The coupling parameters which compose the transformation matrix are estimated by the expectation maximization (EM) principle. The relevance between the hyperparameters is data dependent so the sparsity patterns of neighboring coefficients are related in an adaptive way. Compared with existing block sparse recovery methods, our approach is able to encourage the block sparse structure in a more flexible and more reliable way.

Two-Dimensional Pattern-Coupled Sparse Bayesian Learning via Generalized Approximate Message Passing.

We consider the problem of recovering 2D block-sparse signals with unknown cluster patterns. The 2D block-sparse patterns arise naturally in many practical applications, such as foreground detection and inverse synthetic aperture radar imaging. To exploit the underlying block-sparse structure, we propose a 2D pattern-coupled hierarchical Gaussian prior model. The proposed pattern-coupled hierarchical Gaussian prior model imposes a soft coupling mechanism among neighboring coefficients through their shared hyperparameters. This coupling mechanism enables effective and automatic learning of the underlying irregular cluster patterns, without requiring any a priori knowledge of the block partition of sparse signals. We develop a computationally efficient Bayesian inference method, which integrates the generalized approximate message passing technique with the proposed prior model. Simulation results show that the proposed method offers competitive recovery performance for a range of 2D sparse signal recovery and image processing applications over the existing method, meanwhile achieving a significant reduction in the computational complexity.

Pattern-Coupled Sparse Bayesian Learning for Inverse Synthetic Aperture Radar Imaging

We propose a pattern-coupled sparse Bayesian learning method for inverse synthetic aperture radar (ISAR) imaging by exploiting a block-sparse structure inherent in ISAR target images. A two-dimensional pattern-coupled hierarchical Gaussian prior is proposed to model the pattern dependencies among neighboring scatterers on the target scene. An expectation-maximization (EM) algorithm is developed to infer the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals

We consider the problem of recovering block-sparse signals whose cluster patterns are unknown a priori. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block partition is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. A pattern-coupled hierarchical Gaussian prior is introduced to characterize the pattern dependencies among neighboring coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients. The proposed hierarchical model is similar to that for the conventional sparse Bayesian learning. However, unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also its immediate neighbor hyperparameters. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters are learned by maximizing their posterior probability. We exploit an expectation-maximization (EM) formulation to develop an iterative algorithm that treats the signal as hidden variables and iteratively maximizes a lower bound on the posterior probability. In the M-step, a simple suboptimal solution is employed to replace a gradient-based search to maximize the lower bound. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.