Search Results (64)

We consider the lossless compression bound of any individual data sequence. Conceptually, its Kolmogorov complexity is such a bound yet uncomputable. According to Shannon’s source coding theorem, the average compression bound is $nH$, where n is the number of words and H is the entropy of an oracle probability distribution characterizing the data source. The quantity $nH\left({\widehat{\theta }}_n\right)$ obtained by plugging in the maximum likelihood estimate is an underestimate of the bound. Shtarkov showed that the normalized maximum likelihood (NML) distribution is optimal in a minimax sense for any parametric family. Fitting a data sequence—without any a priori distributional assumption—by a relevant exponential family, we apply the local asymptotic normality to show that the NML code length is $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\int }_{\Theta }{\left|I\left(\theta \right)\right|}^{1/2}d\theta +o\left(1\right)$, where d is dictionary size, $\left|I\right(\theta \left)\right|$ is the determinant of the Fisher information matrix, and $\Theta$ is the parameter space. We demonstrate that sequentially predicting the optimal code length for the next word via a Bayesian mechanism leads to the mixture code whose length is given by $nH\left({\widehat{\theta }}_n\right)+{\displaystyle \frac{d}{2}}log{\displaystyle \frac{n}{2\pi }}+log{\displaystyle \frac{|I\left({\widehat{\theta }}_n\right){|}^{1/2}}{w\left({\widehat{\theta }}_n\right)}}+o\left(1\right)$, where $w\left(\theta \right)$ is a prior. The asymptotics apply to not only discrete symbols but also continuous data if the code length for the former is replaced by the description length for the latter. The analytical result is exemplified by calculating compression bounds of protein-encoding DNA sequences under different parsing models. Typically, compression is maximized when parsing aligns with amino acid codons, while pseudo-random sequences remain incompressible, as predicted by Kolmogorov complexity. Notably, the empirical bound becomes more accurate as the dictionary size increases. Full article

Compressed sensing is widely used in modern resource-constrained sensor networks. However, achieving high-quality and robust signal reconstruction under low sampling rates and noise interference remains challenging. Traditional CS methods have limited performance, so many deep learning-based CS models have been proposed. Although these models show strong fitting capabilities, they often lack the ability to handle complex noise in sensor networks, which affects their performance stability. To address these challenges, this paper proposes SBCS-Net. This framework innovatively expands the iterative process of sparse Bayesian compressed sensing using convolutional neural networks and Transformer. The core of SBCS-Net is to optimize key SBL parameters through end-to-end learning. This can adaptively improve signal sparsity and probabilistically process measurement noise, while fully leveraging the powerful feature extraction and global context modeling capabilities of deep learning modules. To comprehensively evaluate its performance, we conduct systematic experiments on multiple public benchmark datasets. These studies include comparisons with various advanced and traditional compressed sensing methods, comprehensive noise robustness tests, ablation studies of key components, computational complexity analysis, and rigorous statistical significance tests. Extensive experimental results consistently show that SBCS-Net outperforms many mainstream methods in both reconstruction accuracy and visual quality. In particular, it exhibits excellent robustness under challenging conditions such as extremely low sampling rates and strong noise. Therefore, SBCS-Net provides an effective solution for high-fidelity, robust signal recovery in sensor networks and related fields. Full article

Reconfigurable Intelligent Surfaces (RISs) are among the key technologies envisaged for sixth-generation (6G) multiple-input multiple-output (MIMO)–orthogonal frequency division multiplexing (OFDM) wireless systems. However, their passive nature and the frequent absence of a line-of-sight (LoS) path in dense urban environments make uplink channel estimation and localization challenging tasks. Therefore, to achieve channel estimation and localization, this study models the RIS-mobile station (MS) channel as a double-sparse angular structure and proposes a hybrid channel parameter estimation framework for RIS-assisted MIMO-OFDM systems. In the hybrid framework, Simultaneous Orthogonal Matching Pursuit (SOMP) first estimates coarse angular supports. The coarse estimates are refined by a novel refinement stage employing a Variational Bayesian Expectation Maximization (VBEM)-based Off-Grid Sparse Bayesian Learning (OG-SBL) algorithm, which jointly updates azimuth and elevation offsets via Newton-style iterations. An Angle of Arrival (AoA)–Angle of Departure (AoD) matching algorithm is introduced to associate angular components, followed by a 3D localization procedure based on non-LoS (NLoS) multipath geometry. Simulation results show that the proposed framework achieves high angular resolution; high localization accuracy, with 97% of the results within 0.01 m; and a channel estimation error of 0.0046% at 40 dB signal-to-noise ratio (SNR). Full article

The number of hologram points in near-field acoustical holography (NAH) for a vibro-acoustic system plays a vital role in conditioning the transfer function between the source and measuring points. The requirement for many overdetermined hologram points for extended sources to obtain high accuracy poses a problem for the practical applications of NAH. Furthermore, overdetermination does not generally ensure enhanced accuracy, stability, and convergence, owing to the problem of rank deficiency. To achieve satisfactory reconstruction accuracy with underdetermined hologram data, the best practice for choosing hologram points and regularization methods is determined by comparing cross-linked sets of data-sorting and regularization methods. Three typical data selection and treatment methods are compared: iterative discarding of the most dependent data, monitoring singular value changes during the data reduction process, and zero padding in the patch holography technique. To test the regularization method for inverse conditioning, which is used together with the data selection method, the Tikhonov method, Bayesian regularization, and the data compression method are compared. The inverse equivalent source method is chosen as the holography method, and a numerical test is conducted with a point-excited thin plate. The simulation results show that selecting hologram points using the effective independence method, combined with regularization via compressed sensing, significantly reduces the reconstruction error and enhances the modal assurance criterion value. The experimental results also support the proposed best practice for inverting underdetermined hologram data by integrating the NAH data selection and regularization techniques. Full article

This paper presents an integrated approach to developing lightweight, high-performance deep learning models for human activity recognition (HAR) using WiFi Channel State Information (CSI). Motivated by the need for accuracy and efficiency in resource-constrained environments, we combine Bayesian Optimization-based Neural Architecture Search (NAS) with a structured pruning algorithm. NAS identifies optimal network configurations, while pruning systematically removes redundant parameters, preserving accuracy. This approach allows for robust activity recognition from diverse WiFi datasets under varying conditions. Experimental results across multiple benchmark datasets demonstrate that our method not only maintains but often improves accuracy after pruning, resulting in models that are both smaller and more accurate. This offers a scalable and adaptable solution for real-world deployments in IoT and mobile platforms, achieving an optimal balance of efficiency and accuracy in HAR using WiFi CSI. Full article

The rapid and accurate reconstruction of the high-resolution range profiles (HRRPs) of high-speed targets from incomplete wideband radar echoes is a critical component in space target recognition tasks (STRTs). However, state-of-the-art HRRP reconstruction algorithms based on sparse Bayesian learning (SBL) are computationally expensive and require the manual selection of prior scale parameters. To address these challenges, this paper proposes a model-driven deep network based on fast mean-field SBL (FMFSBL-Net) for the HRRP reconstruction of high-speed targets under missing data conditions. Specifically, we integrate a precise velocity compensation and HRRP reconstruction into the mean-field SBL framework, which introduces a unified SBL objective function and a mean-field variational family to avoid matrix inversion operations. To reduce the performance loss caused by mismatched prior scale parameters, we unfold the limited FMFSBL iterative process into a deep network, learning the optimal global prior scale parameters through training. Additionally, we introduce a sparsity-enhanced loss function to improve the quality and noise robustness of HRRPs. In addition, simulation and measurement experimental results show that the proposed FMFSBL-Net has a superior reconstruction performance and computational efficiency compared to FMFSBL and existing state-of-the-art SBL framework type algorithms. Full article

It is challenging to estimate the elevation angle of low-altitude targets due to the multipath effect. Various signal processing techniques have been proposed to mitigate these effects, including the use of multi-frequency signals as opposed to single narrowband signals. However, the optimal type of multi-frequency signals and their effective utilization have not been thoroughly explored. Compressive sensing was also proposed as a high-resolution angle estimation method. But, that was conducted with narrowband signals. In this paper, we employ MIMO-OFDM signals along with a block sparse Bayesian learning fast marginalized (BSBL-FM) method. This combination allows for the effective processing of multi-frequency signals and provides high resolution estimates. The MIMO-OFDM approach represents radar signals in a block-sparse matrix form, and the BSBL-FM method leverages this sparsity to achieve high-resolution angle estimates. Simulation results demonstrate that our method can accurately estimate angles at extremely low altitudes where the elevation angle is less than 1 degree. Full article

Through extensive literature review, it has been found that sparse Bayesian learning (SBL) is mainly applied to traditional scalar hydrophones and is rarely applied to vector hydrophones. This article proposes a direction of arrival (DOA) estimation method for vector hydrophones based on SBL (Vector-SBL). Firstly, vector hydrophones capture both sound pressure and particle velocity, enabling the acquisition of multidimensional sound field information. Secondly, SBL accurately reconstructs the received vector signal, addressing challenges like low signal-to-noise ratio (SNR), limited snapshots, and coherent sources. Finally, precise DOA estimation is achieved for multiple sources without prior knowledge of their number. Simulation experiments have shown that compared with the OMP, MUSIC, and CBF algorithms, the proposed method exhibits higher DOA estimation accuracy under conditions of low SNR, small snapshots, multiple sources, and coherent sources. Furthermore, it demonstrates superior resolution when dealing with closely spaced signal sources. Full article

Off-grid issues and high computational complexity are two major challenges faced by sparse Bayesian learning (SBL)-based compressive sensing (CS) algorithms used for random frequency pulse interval agile (RFPA) radar. Therefore, this paper proposes an off-grid CS algorithm for RFPA radar based on Root-SBL to address these issues. To effectively cope with off-grid issues, this paper derives a root-solving formula inspired by the Root-SBL algorithm for velocity parameters applicable to RFPA radar, thus enabling the proposed algorithm to directly solve the velocity parameters of targets during the fine search stage. Meanwhile, to ensure computational feasibility, the proposed algorithm utilizes a simple single-level hierarchical prior distribution model and employs the derived root-solving formula to avoid the refinement of velocity grids. Moreover, during the fine search stage, the proposed algorithm combines the fixed-point strategy with the Expectation-Maximization algorithm to update the hyperparameters, further reducing computational complexity. In terms of implementation, the proposed algorithm updates hyperparameters based on the single-level prior distribution to approximate values for the range and velocity parameters during the coarse search stage. Subsequently, in the fine search stage, the proposed algorithm performs a grid search only in the range dimension and uses the derived root-solving formula to directly solve for the target velocity parameters. Simulation results demonstrate that the proposed algorithm maintains low computational complexity while exhibiting stable performance for parameter estimation in various multi-target off-grid scenarios. Full article

With the increasingly complex electromagnetic environment faced by radar, random stepped frequency (RSF) has garnered widespread attention owing to its remarkable Electronic Counter-Countermeasure (ECCM) characteristic, and it has been universally applied in inverse synthetic aperture radar (ISAR) in recent years. However, if the phase error induced by the translational motion of the target in RSF ISAR is not precisely compensated, the imaging result will be defocused. To address this challenge, a novel 2D method based on sparse Bayesian learning, denoted as 2D-autofocusing complex-value inverse-free SBL (2D-AFCIFSBL), is proposed to accomplish joint ISAR imaging and autofocusing for RSF ISAR. First of all, to integrate autofocusing into the ISAR imaging process, phase error estimation is incorporated into the imaging model. Then, we increase the speed of Bayesian inference by relaxing the evidence lower bound (ELBO) to avoid matrix inversion, and we further convert the iterative process into a matrix form to improve the computational efficiency. Finally, the 2D phase error is estimated through maximum likelihood estimation (MLE) in the image reconstruction iteration. Experimental results on both simulated and measured datasets have substantiated the effectiveness and computational efficiency of the proposed 2D joint imaging and autofocusing method. Full article

A novel compressive sensing (CS) synthetic-aperture radar (SAR) called AgileSAR has been proposed to increase swath width for sparse scenes while preserving azimuthal resolution. AgileSAR overcomes the limitation of the Nyquist sampling theorem so that it has a small amount of data and low system complexity. However, traditional CS optimization-based algorithms suffer from manual tuning and pre-definition of optimization parameters, and they generally involve high time and computational complexity for AgileSAR imaging. To address these issues, a pseudo-${\mathcal{L}}_0$-norm fast iterative shrinkage algorithm network (pseudo-${\mathcal{L}}_0$-norm FISTA-net) is proposed for AgileSAR imaging via the deep unfolding network in this paper. Firstly, a pseudo-${\mathcal{L}}_0$-norm regularization model is built by taking an approximately fair penalization rule based on Bayesian estimation. Then, we unfold the operation process of FISTA into a data-driven deep network to solve the pseudo-${\mathcal{L}}_0$-norm regularization model. The network’s parameters are automatically learned, and the learned network significantly increases imaging speed, so that it can improve the accuracy and efficiency of AgileSAR imaging. In addition, the nonlinearly sparsifying transform can learn more target details than the traditional sparsifying transform. Finally, the simulated and data experiments demonstrate the superiority and efficiency of the pseudo-${\mathcal{L}}_0$-norm FISTA-net for AgileSAR imaging. Full article

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar. Full article

The direction-of-arrival (DOA) estimation is predominantly influenced by the antenna’s aperture size. However, space constraints on flight platforms often necessitate the use of antennas with smaller apertures and fewer array elements. This inevitably imposes limitations on the DOA estimation’s resolution and degrees of freedom. To address these precision constraints, we introduce an accurate DOA estimation method based on spatial synthetic aperture model. This method adopts a two-stage strategy to ensure both efficiency and precision in DOA estimation. Initially, the orthogonal matching pursuit (OMP) reconstruction algorithm processes the original aperture data, providing a rough estimate of target angles that guides the aircraft’s flight direction. Subsequently, the early estimations merge with the aircraft’s motion space samples, forming equivalent spatially synthesized array samples. The refined angle estimation then employs the OMP-RELAX algorithm. Moreover, with the off-grid issue in mind, we devise an estimation method integrating Bayesian parameter estimation with dictionary sequence refinement. The proposed technique harnesses the spatial synthetic aperture for pinpoint estimation, effectively addressing the challenges of atomic orthogonality and angular off-grid on estimation accuracy. Importantly, the efficiency of deploying sparse reconstruction for angle estimation is bolstered by our phased strategy, eliminating the necessity for fine grid analysis across the entire observation scene. Moreover, the poor estimation accuracy caused by coherent source targets and angular-flickering targets is improved by sparse reconstruction. Through simulation and experiment, we affirm the proposed method’s efficacy in angle estimation. The results indicate that target angle estimation errors are limited to within 1°. Furthermore, we assess the impact of variables such as target state, heading angle, spatial sampling points, and target distance on the estimation accuracy of our method, showcasing its resilience and adaptability. Full article

Magnetic Resonance Imaging (MRI) is an essential medical imaging modality that provides excellent soft-tissue contrast and high-resolution images of the human body, allowing us to understand detailed information on morphology, structural integrity, and physiologic processes. However, MRI exams usually require lengthy acquisition times. Methods such as parallel MRI and Compressive Sensing (CS) have significantly reduced the MRI acquisition time by acquiring less data through undersampling k-space. The state-of-the-art of fast MRI has recently been redefined by integrating Deep Learning (DL) models with these undersampled approaches. This Systematic Literature Review (SLR) comprehensively analyzes deep MRI reconstruction models, emphasizing the key elements of recently proposed methods and highlighting their strengths and weaknesses. This SLR involves searching and selecting relevant studies from various databases, including Web of Science and Scopus, followed by a rigorous screening and data extraction process using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. It focuses on various techniques, such as residual learning, image representation using encoders and decoders, data-consistency layers, unrolled networks, learned activations, attention modules, plug-and-play priors, diffusion models, and Bayesian methods. This SLR also discusses the use of loss functions and training with adversarial networks to enhance deep MRI reconstruction methods. Moreover, we explore various MRI reconstruction applications, including non-Cartesian reconstruction, super-resolution, dynamic MRI, joint learning of reconstruction with coil sensitivity and sampling, quantitative mapping, and MR fingerprinting. This paper also addresses research questions, provides insights for future directions, and emphasizes robust generalization and artifact handling. Therefore, this SLR serves as a valuable resource for advancing fast MRI, guiding research and development efforts of MRI reconstruction for better image quality and faster data acquisition. Full article

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. Full article