Movable antennas (MAs) are a promising technology to achieve a significant enhancement in rate for future wireless networks. The pioneering investigation on near-field directional modulation design for a reconfigurable intelligent surface (RIS)-assisted MA system is presented, with the base station equipped with a MA array. To maximize the secrecy sum rate (Max-SSR) with hardware impairments (HWIs) and imperfect channel state information (CSI), which involves a joint optimization of beamforming vectors for confidential messages and artificial noise (AN), power allocation factors, phase shift matrices, MA positions, and receive beamforming vectors. Firstly, the transmit beamforming vectors and phase shift matrices are iteratively optimized, leveraging leakage theory and phase alignment techniques. Then, two novel algorithms for discrete MA positioning are proposed, respectively, employing uniform and compressed sensing (CS)-based non-uniform grouping strategies. Subsequently, the AN is considered and designed as the additional energy required for zero-space projection, and the receive beamforming vector is derived using the minimum mean square error (MMSE) method. The proposed algorithms have low computational complexity. Simulation results demonstrate the effectiveness of the proposed algorithms. Under HWIs and imperfect CSI, the proposed algorithm can achieve a 28\% enhancement in SSR performance while reducing the number of antennas by 37.5\% compared to traditional fixed-position antenna (FPA) systems.
Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union of subspaces. The extension allows for handling more complex signal structures and broadens the framework to tasks like compressed sensing. These mismatches between samples and channels often arise in applications such as whole-brain calcium imaging of freely moving organisms or multi-target tracking. We improve over previous models by deriving tighter bounds on the required number of samples for unique reconstruction, while supporting more general signal types. The approach is validated through an application in whole-brain calcium imaging, where organism movements disrupt sample-to-neuron mappings. This demonstrates the utility of our framework in real-world settings with imprecise sample-channel associations, achieving accurate signal reconstruction.
Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem. To tackle this challenge, the straight-through estimator (STE) has become the most widely adopted heuristic, allowing backpropagation through discrete operations by introducing surrogate gradients. However, its theoretical properties remain largely unexplored, with few existing works simplifying the analysis by assuming an infinite amount of training data. In contrast, this work presents the first finite-sample analysis of STE in the context of neural network quantization. Our theoretical results highlight the critical role of sample size in the success of STE, a key insight absent from existing studies. Specifically, by analyzing the quantization-aware training of a two-layer neural network with binary weights and activations, we derive the sample complexity bound in terms of the data dimensionality that guarantees the convergence of STE-based optimization to the global minimum. Moreover, in the presence of label noises, we uncover an intriguing recurrence property of STE-gradient method, where the iterate repeatedly escape from and return to the optimal binary weights. Our analysis leverages tools from compressed sensing and dynamical systems theory.
Efficient solutions to inverse problems often require supervised training with labeled data to model posterior distributions, such as using conditional diffusion models in seismic applications. However, these methods are problem-specific and involve substantial computational costs for retraining on each new task. To address these limitations, we propose a novel approach that first trains a robust unconditional diffusion model for generative seismic data modeling and then leverages the pre-trained model for posterior sampling across various seismic inverse problems. This method enables efficient sampling without the need for task-specific conditional models, offering a scalable and flexible solution for seismic applications. The effectiveness of our approach is demonstrated through unconditional sampling of seismic data and posterior sampling in three noisy inverse problems—denoising, interpolation, and compressed sensing.
The concept of Compressed Sensing-aided Space-Frequency Index Modulation (CS-SFIM) is conceived for the Large-Scale Multi-User Multiple-Input Multiple-Output Uplink (LS-MU-MIMO-UL) of Next-Generation (NG) networks. Explicitly, in CS-SFIM, the information bits are mapped to both spatial- and frequency-domain indices, where we treat the activation patterns of the transmit antennas and of the subcarriers separately. Serving a large number of users in an MU-MIMO-UL system leads to substantial Multi-User Interference (MUI). Hence, we design the Space-Frequency (SF) domain matrix as a joint factor graph, where the Approximate Message Passing (AMP) and Expectation Propagation (EP) based MU detectors can be utilized. In the LS-MU-MIMO-UL scenario considered, the proposed system uses optimal Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detectors as benchmarks for comparison with the proposed MP-based detectors. These MP-based detectors significantly reduce the detection complexity compared to ML detection, making the design eminently suitable for LS-MU scenarios. To further reduce the detection complexity and improve the detection performance, we propose a pair of Graph Neural Network (GNN) based detectors, which rely on the orthogonal AMP (OAMP) and on the EP algorithm, which we refer to as the GNN-AMP and GEPNet detectors, respectively. The GEPNet detector maximizes the detection performance, while the GNN-AMP detector strikes a performance versus complexity trade-off. The GNN is trained for a single system configuration and yet it can be used for any number of users in the system. The simulation results show that the GNN-based detector approaches the ML performance in various configurations.
We introduce the Sparse pretrained Radio Transformer (SpaRTran), an unsupervised representation learning approach based on the concept of compressed sensing for radio channels. Our approach learns embeddings that focus on the physical properties of radio propagation, to create the optimal basis for fine-tuning on radio-based downstream tasks. SpaRTran uses a sparse gated autoencoder that induces a simplicity bias to the learned representations, resembling the sparse nature of radio propagation. For signal reconstruction, it learns a dictionary that holds atomic features, which increases flexibility across signal waveforms and spatiotemporal signal patterns. Our experiments show that SpaRTran reduces errors by up to 85 % compared to state-of-the-art methods when fine-tuned on radio fingerprinting, a challenging downstream task. In addition, our method requires less pretraining effort and offers greater flexibility, as we train it solely on individual radio signals. SpaRTran serves as an excellent base model that can be fine-tuned for various radio-based downstream tasks, effectively reducing the cost for labeling. In addition, it is significantly more versatile than existing methods and demonstrates superior generalization.
This paper investigates the near-field (NF) channel estimation (CE) for extremely large-scale multiple-input multiple-output (XL-MIMO) systems. Considering the pronounced NF effects in XL-MIMO communications, we first establish a joint angle-distance (AD) domain-based spherical-wavefront physical channel model that captures the inherent sparsity of XL-MIMO channels. Leveraging the channel's sparsity in the joint AD domain, the CE is approached as a task of reconstructing sparse signals. Anchored in this framework, we first propose a compressed sensing algorithm to acquire a preliminary channel estimate. Harnessing the powerful implicit prior learning capability of generative artificial intelligence (GenAI), we further propose a GenAI-based approach to refine the estimated channel. Specifically, we introduce the preliminary estimated channel as side information, and derive the evidence lower bound (ELBO) of the log-marginal distribution of the target NF channel conditioned on the preliminary estimated channel, which serves as the optimization objective for the proposed generative diffusion model (GDM). Additionally, we introduce a more generalized version of the GDM, the non-Markovian GDM (NM-GDM), to accelerate the sampling process, achieving an approximately tenfold enhancement in sampling efficiency. Experimental results indicate that the proposed approach is capable of offering substantial performance gain in CE compared to existing benchmark schemes within NF XL-MIMO systems. Furthermore, our approach exhibits enhanced generalization capabilities in both the NF or far-field (FF) regions.
Recent advances in deep learning-based parallel compressed sensing magnetic resonance imaging (p-CSMRI) have significantly improved reconstruction quality. However, current p-CSMRI methods often require training separate deep neural network (DNN) for each organ due to anatomical variations, creating a barrier to developing generalized medical image reconstruction systems. To address this, we propose CAPNet (cross-organ all-in-one deep unfolding p-CSMRI network), a unified framework that implements a p-CSMRI iterative algorithm via three specialized modules: auxiliary variable module, prior module, and data consistency module. Recognizing that p-CSMRI systems often employ varying sampling ratios for different organs, resulting in organ-specific artifact patterns, we introduce an artifact generation submodule, which extracts and integrates artifact features into the data consistency module to enhance the discriminative capability of the overall network. For the prior module, we design an organ structure-prompt generation submodule that leverages structural features extracted from the segment anything model (SAM) to create cross-organ prompts. These prompts are strategically incorporated into the prior module through an organ structure-aware Mamba submodule. Comprehensive evaluations on a cross-organ dataset confirm that CAPNet achieves state-of-the-art reconstruction performance across multiple anatomical structures using a single unified model. Our code will be published at https://github.com/shibaoshun/CAPNet.
In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach.
We consider stacked intelligent metasurfaces (SIMs) as a tool to improve the performance of bistatic integrated sensing and communications (ISAC) schemes. To that end, we optimize the SIMs and design a radar parameter estimation (RPE) scheme aimed at enhancing radar sensing capabilities as well as communication performance under ISAC-enabling waveforms known to perform well in doubly-dispersive (DD) channels. The SIM optimization is done via a min-max problem formulation solved via steepest ascent with closed-form gradients, while the RPE is carried out via a compressed sensing-based probabilistic data association (PDA) algorithm. Our numerical results indicate that the design of waveforms suitable to mitigating the effects of DD channels is significantly impacted by the emerging SIM technology.
The trend in modern science and technology is to take vector measurements rather than scalars, ruthlessly scaling to ever higher dimensional vectors. For about two decades now, traditional scalar Compressed Sensing has been synonymous with a Convex Optimization based procedure called Basis Pursuit. In the vector recovery case, the natural tendency is to return to a straightforward vector extension of Basis Pursuit, also based on Convex Optimization. However, Convex Optimization is provably suboptimal, particularly when $B$ is large. In this paper, we propose SteinSense, a lightweight iterative algorithm, which is provably optimal when $B$ is large. It does not have any tuning parameter, does not need any training data, requires zero knowledge of sparsity, is embarrassingly simple to implement, and all of this makes it easily scalable to high vector dimensions. We conduct a massive volume of both real and synthetic experiments that confirm the efficacy of SteinSense, and also provide theoretical justification based on ideas from Approximate Message Passing. Fascinatingly, we discover that SteinSense is quite robust, delivering the same quality of performance on real data, and even under substantial departures from conditions under which existing theory holds.
Compressed sensing Synthetic Aperture Radar (SAR) image formation, formulated as an inverse problem and solved with traditional iterative optimization methods can be very computationally expensive. We investigate the use of denoising diffusion probabilistic models for compressive SAR image reconstruction, where the diffusion model is guided by a poor initial reconstruction from sub-sampled data obtained via standard imaging methods. We present results on real SAR data and compare our compressively sampled diffusion model reconstruction with standard image reconstruction methods utilizing the full data set, demonstrating the potential performance gains in imaging quality.
This work considers the three-dimensional (3-D) positioning problem in a Terahertz (THz) system enabled by a modular extra-large (XL) array with sub-connected architecture. Our purpose is to estimate the Cartesian Coordinates of multiple user equipments (UEs) with the received signal of the RF chains while considering the spatial non-stationarity (SNS). We apply the hybrid spherical-planar wave model (HSPWM) as the channel model owing to the structual feature of the modular array, and propose a 3-D localization algorithm with relatively high accuracy and low complexity. Specifically, we first distinguish the visible sub-arrays (SAs) located in the VR and estimate the angles-of-arrival (AoAs) from each UE to typical visible SAs with the largest receive power via compressed sensing (CS) method. In addition, we apply the weighted least square (WLS) method to obtain a coarse 3-D position estimation of each UE according to the AoA estimations. Then, we estimate the AoAs of the other SAs with a reduced dictionary (RD)-CS-based method for lower computational complexity, and utilize all the efficient AoA estimations to derive a fine position estimation. Simulation results indicate that the proposed positioning framework based on modular XL-array can achieve satisfactory accuracy with evident reduction in complexity. Furthermore, the deployment of SAs and the allocation of antenna elements need to be specially designed for better positioning performance.
The sub-Nyquist radar framework exploits the sparsity of signals, which effectively alleviates the pressure on system storage and transmission bandwidth. Compressed sensing (CS) algorithms, such as the VAMP algorithm, are used for sparse signal processing in the sub-Nyquist radar framework. By combining deep unfolding techniques with VAMP, faster convergence and higher accuracy than traditional CS algorithms are achieved. However, deep unfolding disrupts the parameter constrains in traditional VAMP algorithm, leading to the distribution of non-sparse noisy estimation in VAMP deep unfolding unknown, and its distribution parameter unable to be obtained directly using method of traditional VAMP, which prevents the application of VAMP deep unfolding in radar constant false alarm rate (CFAR) detection. To address this problem, we explore the distribution of the non-sparse noisy estimation and propose a parameter convergence detector (PCD) to achieve CFAR detection based on VAMP deep unfolding. Compared to the state-of-the-art methods, PCD leverages not only the sparse solution, but also the non-sparse noisy estimation, which is used to iteratively estimate the distribution parameter and served as the test statistic in detection process. In this way, the proposed algorithm takes advantage of both the enhanced sparse recovery accuracy from deep unfolding and the distribution property of VAMP, thereby achieving superior CFAR detection performance. Additionally, the PCD requires no information about the power of AWGN in the environment, which is more suitable for practical application. The convergence performance and effectiveness of the proposed PCD are analyzed based on the Banach Fixed-Point Theorem. Numerical simulations and practical data experiments demonstrate that PCD can achieve better false alarm control and target detection performance.
Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused by the measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming that the noise is Gaussian. We moreover provide similar guarantees for measurements sampled with-replacement with arbitrary probability weights. All our results hold on prior sets contained in a union of low-dimensional subspaces. Finally, we demonstrate that this denoising behavior appears in empirical experiments with a rate that closely matches our theoretical guarantees when the prior set is the range of a generative ReLU neural network and when it is the set of sparse vectors.
Integrated sensing and communication (ISAC) is envisioned be to one of the paradigms upon which next-generation mobile networks will be built, extending localization and tracking capabilities, as well as giving birth to environment-aware wireless access. A key aspect of sensing integration is parameter estimation, which involves extracting information about the surrounding environment, such as the direction, distance, and velocity of various objects within. This is typically of a high-dimensional nature, which leads to significant computational complexity, if performed jointly across multiple sensing dimensions, such as space, frequency, and time. Additionally, due to the incorporation of sensing on top of the data transmission, the time window available for sensing is likely to be short, resulting in an estimation problem where only a single snapshot is accessible. In this work, we propose PLAIN, a tensor-based estimation architecture that flexibly scales with multiple sensing dimensions and can handle high dimensionality, limited measurement time, and super-resolution requirements. It consists of three stages: a compression stage, where the high dimensional input is converted into lower dimensionality, without sacrificing resolution; a decoupled estimation stage, where the parameters across the different dimensions are estimated in parallel with low complexity; an input-based fusion stage, where the decoupled parameters are fused together to form a paired multidimensional estimate. We investigate the performance of the architecture for different configurations and compare it against practical sequential and joint estimation baselines, as well as theoretical bounds. Our results show that PLAIN, using tools from tensor algebra, subspace-based processing, and compressed sensing, can scale flexibly with dimensionality, while operating with low complexity and maintaining super-resolution.
This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be expressed as a power of a seminorm. We then show that such functionals can be approximated to arbitrary precision with the help of polyhedral norms. In particular, we identify two dual parameterizations of such systems: (i) a synthesis form with an $\ell_1$-penalty that involves some learnable dictionary; and (ii) an analysis form with an $\ell_\infty$-penalty that involves a trainable regularization operator. After having provided geometric insights and proved that the two forms are universal, we propose an implementation that relies on a specific architecture (tight frame with a weighted $\ell_1$ penalty) that is easy to train. We illustrate its use for denoising and the reconstruction of biomedical images. We find that the proposed framework outperforms the sparsity-based methods of compressed sensing, while it offers essentially the same convergence and robustness guarantees.
Recent advances in Latent Video Diffusion Models (LVDMs) have revolutionized video generation by leveraging Video Variational Autoencoders (Video VAEs) to compress intricate video data into a compact latent space. However, as LVDM training scales, the computational overhead of Video VAEs becomes a critical bottleneck, particularly for encoding high-resolution videos. To address this, we propose LeanVAE, a novel and ultra-efficient Video VAE framework that introduces two key innovations: (1) a lightweight architecture based on a Neighborhood-Aware Feedforward (NAF) module and non-overlapping patch operations, drastically reducing computational cost, and (2) the integration of wavelet transforms and compressed sensing techniques to enhance reconstruction quality. Extensive experiments validate LeanVAE's superiority in video reconstruction and generation, particularly in enhancing efficiency over existing Video VAEs. Our model offers up to 50x fewer FLOPs and 44x faster inference speed while maintaining competitive reconstruction quality, providing insights for scalable, efficient video generation. Our models and code are available at https://github.com/westlake-repl/LeanVAE
Compressed sensing (CS)-based techniques have been widely applied in the grant-free non-orthogonal multiple access (NOMA) to a single-antenna base station (BS). In this paper, we consider the multi-antenna reception at the BS for uplink grant-free access for the massive machine type communication (mMTC) with limited channel resources. To enhance the overloading performance of the BS, we develop a general framework for the synergistic amalgamation of the spatial division multiple access (SDMA) technique with the CS-based grant-free NOMA. We derive a closed-form statistical beamforming and a dynamic beamforming scheme for the inter-cluster interference suppression when applying SDMA. Based on this, we further develop a joint adaptive beamforming and subspace pursuit (JABF-SP) algorithm for the multiuser detection and data recovery, with a novel sparsity level decision method without the accurate knowledge of the noise level. To further improve the data recovery performance, we propose an interference cancellation based J-ABF-SP scheme (J-ABF-SP-IC) by using the initial signal estimates generated from the J-ABF-SP algorithm. Illustrative simulations verify the superior user detection and signal recovery performance of our proposed algorithms in comparison with existing CS-based grant-free NOMA techniques.
The detection of irregularly spaced pulses of non-negligible width is a fascinating yet under-explored topic in signal processing. It sits adjacent to other core topics such as radar and symbol detection yet has its own distinctive challenges. Even modern techniques such as compressed sensing perform worse than may be expected on pulse processing problems. Real-world applications include nuclear spectroscopy, flow cytometry, seismic signal processing and neural spike sorting, and these in turn have applications to environmental radiation monitoring, surveying, diagnostic medicine, industrial imaging, biomedical imaging, top-down proteomics, and security screening, to name just a few. This overview paper endeavours to position the pulse processing problem in the context of signal processing. It also describes some current challenges in the field.