Sparse Reconstruction of Sound Field Using Bayesian Compressive Sensing and Equivalent Source Method.

To solve the problem of sound field reconstruction with fewer measurement points, a sound field reconstruction method based on Bayesian compressive sensing is proposed. In this method, a sound field reconstruction model based on a combination of the equivalent source method and sparse Bayesian compressive sensing is established. The MacKay iteration of the relevant vector machine is used to infer the hyperparameters and estimate the maximum a posteriori probability of both the sound source strength and noise variance. The optimal solution for sparse coefficients with an equivalent sound source is determined to achieve the sparse reconstruction of the sound field. The numerical simulation results demonstrate that the proposed method has higher accuracy over the entire frequency range compared to the equivalent source method, indicating a better reconstruction performance and wider frequency applicability with undersampling. Moreover, in environments with low signal-to-noise ratios, the proposed method exhibits significantly lower reconstruction errors than the equivalent source method, indicating a superior anti-noise performance and greater robustness in sound field reconstruction. The experimental results further verify the superiority and reliability of the proposed method for sound field reconstruction with limited measurement points.

Resolution Enhancement for Millimeter-Wave Radar ROI Image with Bayesian Compressive Sensing.

For millimeter-wave (MMW) imaging security systems, the image resolution promisingly determines the performance of suspicious target detection and recognition. Conventional synthetic aperture radar (SAR) imaging algorithms only provide limited resolution in active MMW imaging, which is limited by the system. In terms of enhancing the resolution of a region of interest (ROI) image containing suspicious targets, super-resolution (SR) imaging is adopted via Bayesian compressive sensing (BCS) implemented by fast Fourier transform (FFT). The spatial sparsity of MMW ROI images is well exploited with BCS to achieve resolution enhancement without computational cost. Both simulated and measured experiments confirm that the proposed scheme effectively improves the resolution of ROI images.

A Sound Source Identification Algorithm Based on Bayesian Compressive Sensing and Equivalent Source Method.

Near-field acoustic holography (NAH) based on equivalent source method (ESM) is an effective method for identifying sound sources. Conventional ESM focuses on relatively low frequencies and cannot provide a satisfactory solution at high frequencies. So its improved method called wideband acoustic holography (WBH) has been proposed, which has high reconstruction accuracy at medium-to-high frequencies. However, it is less accurate for coherent sound sources at low frequencies. To improve the reconstruction accuracy of conventional ESM and WBH, a sound source identification algorithm based on Bayesian compressive sensing (BCS) and ESM is proposed. This method uses a hierarchical Laplace sparse prior probability distribution, and adaptively adjusts the regularization parameter, so that the energy is concentrated near the correct equivalent source. Referring to the function beamforming idea, the original algorithm with order v can improve its dynamic range, and then more accurate position information is obtained. Based on the simulation of irregular microphone array, comparisons with conventional ESM and WBH show that the proposed method is more accurate, suitable for a wider range of frequencies, and has better reconstruction performance for coherent sources. By increasing the order v, the coherent sources can be located accurately. Finally, the stability and reliability of the proposed method are verified by experiments.

Two-Tier PSO Based Data Routing Employing Bayesian Compressive Sensing in Underwater Sensor Networks.

Underwater acoustic sensor networks play an important role in assisting humans to explore information under the sea. In this work, we consider the combination of sensor selection and data routing in three dimensional underwater wireless sensor networks based on Bayesian compressive sensing and particle swarm optimization. The algorithm we proposed is a two-tier PSO approach. In the first tier, a PSO-based clustering protocol is proposed to synthetically consider the energy consumption and uniformity of cluster head distribution. Then in the second tier, a PSO-based routing protocol is proposed to implement inner-cluster one-hop routing and outer-cluster multi-hop routing. The nodes selected to constitute i-th effective routing path decide which positions in the i-th row of the measurement matrix are nonzero. As a result, in this tier the protocol comprehensively considers energy efficiency, network balance and data recovery quality. The Bayesian Cramér-Rao Bound (BCRB) in such a case is analyzed and added in the fitness function to monitor the mean square error of the reconstructed signal. The experimental results validate that our algorithm maintains a longer life time and postpones the appearance of the first dead node while keeps the reconstruction error lower compared with the cutting-edge algorithms which are also based on distributed multi-hop compressive sensing approaches.

Wideband Spectrum Sensing: A Bayesian Compressive Sensing Approach.

Sensing the wideband spectrum is an important process for next-generation wireless communication systems. Spectrum sensing primarily aims at detecting unused spectrum holes over wide frequency bands so that secondary users can use them to meet their requirements in terms of quality-of-service. However, this sensing process requires a great deal of time, which is not acceptable for timely communications. In addition, the sensing measurements are often affected by uncertainty. In this paper, we propose an approach based on Bayesian compressive sensing to speed up the process of sensing and to handle uncertainty. This approach takes only a few measurements using a Toeplitz matrix, recovers the wideband signal from a few measurements using Bayesian compressive sensing via fast Laplace prior, and detects either the presence or absence of the primary user using an autocorrelation-based detection method. The proposed approach was implemented using GNU Radio software and Universal Software Radio Peripheral units and was tested on real-world signals. The results show that the proposed approach speeds up the sensing process by minimizing the number of samples while achieving the same performance as Nyquist-based sensing techniques regarding both the probabilities of detection and false alarm.

Multi-Frequency GPR Microwave Imaging of Sparse Targets through a Multi-Task Bayesian Compressive Sensing Approach.

An innovative inverse scattering (IS) method is proposed for the quantitative imaging of pixel-sparse scatterers buried within a lossy half-space. On the one hand, such an approach leverages on the wide-band nature of ground penetrating radar (GPR) data by jointly processing the multi-frequency (MF) spectral components of the collected radargrams. On the other hand, it enforces sparsity priors on the problem unknowns to yield regularized solutions of the fully non-linear scattering equations. Towards this end, a multi-task Bayesian compressive sensing (MT-BCS) methodology is adopted and suitably customized to take full advantage of the available frequency diversity and of the a-priori information on the class of imaged targets. Representative results are reported to assess the proposed MF-MT-BCS strategy also in comparison with competitive state-of-the-art alternatives.

Full-Vectorial 3D Microwave Imaging of Sparse Scatterers through a Multi-Task Bayesian Compressive Sensing Approach.

In this paper, the full-vectorial three-dimensional (3D) microwave imaging (MI) of sparse scatterers is dealt with. Towards this end, the inverse scattering (IS) problem is formulated within the contrast source inversion (CSI) framework and it is aimed at retrieving the sparsest and most probable distribution of the contrast source within the imaged volume. A customized multi-task Bayesian compressive sensing (MT-BCS) method is used to yield regularized solutions of the 3D-IS problem with a remarkable computational efficiency. Selected numerical results on representative benchmarks are presented and discussed to assess the effectiveness and the reliability of the proposed MT-BCS strategy in comparison with other competitive state-of-the-art approaches, as well.