Compressive sensing is a promising solution for the channel estimation in multiple-input multiple-output (MIMO) systems with large antenna arrays and constrained hardware. Utilizing site-specific channel data from real-world systems, deep learning can be employed to learn the compressive sensing measurement vectors with minimum redundancy, thereby focusing sensing power on promising spatial directions of the channel. Collecting real-world channel data, however, is challenging due to the high overhead resulting from the large number of antennas and hardware constraints. In this paper, we propose leveraging a site-specific digital twin to generate synthetic channel data, which shares a similar distribution with real-world data. The synthetic data is then used to train the deep learning models for learning measurement vectors and hybrid precoder/combiner design in an end-to-end manner. We further propose a model refinement approach to fine-tune the model pre-trained on the digital twin data with a small amount of real-world data. The evaluation results show that, by training the model on the digital twin data, the learned measurement vectors can be efficiently adapted to the environment geometry, leading to high performance of hybrid precoding for real-world deployments. Moreover, the model refinement approach can enable the digital twin aided model to achieve comparable performance to the model trained on the real-world dataset with a significantly reduced amount of real-world data.
Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for future wireless systems. In this paper, we develop a novel scheme that utilizes orthogonal frequency division multiplexing (OFDM) pilot signals to sense the electromagnetic (EM) property of the target and thus identify the materials of the target. Specifically, we first establish an EM wave propagation model with Maxwell equations, where the EM property of the target is captured by a closed-form expression of the channel. We then build the mathematical model for the relative permittivity and conductivity distribution (RPCD) within a predetermined region of interest shared by multiple base stations (BSs). Based on the EM wave propagation model, we propose an EM property sensing method, in which the RPCD can be reconstructed from compressive sensing techniques that exploits the joint sparsity structure of the EM property vector. We then develop a fusion algorithm to combine data from multiple BSs, which can enhance the reconstruction accuracy of EM property by efficiently integrating diverse measurements. Moreover, the fusion is performed at the feature level of RPCD and features low transmission overhead. We further design the pilot signals that can minimize the mutual coherence of the equivalent channels and enhance the diversity of incident EM wave patterns. Simulation results demonstrate the efficacy of the proposed method in achieving high-quality RPCD reconstruction and accurate material classification.
Inverse imaging problems (IIPs) arise in various applications, with the main objective of reconstructing an image from its compressed measurements. This problem is often ill-posed for being under-determined with multiple interchangeably consistent solutions. The best solution inherently depends on prior knowledge or assumptions, such as the sparsity of the image. Furthermore, the reconstruction process for most IIPs relies significantly on the imaging (i.e. forward model) parameters, which might not be fully known, or the measurement device may undergo calibration drifts. These uncertainties in the forward model create substantial challenges, where inaccurate reconstructions usually happen when the postulated parameters of the forward model do not fully match the actual ones. In this work, we devoted to tackling accurate reconstruction under the context of a set of possible forward model parameters that exist. Here, we propose a novel Moment-Aggregation (MA) framework that is compatible with the popular IIP solution by using a neural network prior. Specifically, our method can reconstruct the signal by considering all candidate parameters of the forward model simultaneously during the update of the neural network. We theoretically demonstrate the convergence of the MA framework, which has a similar complexity with reconstruction under the known forward model parameters. Proof-of-concept experiments demonstrate that the proposed MA achieves performance comparable to the forward model with the known precise parameter in reconstruction across both compressive sensing and phase retrieval applications, with a PSNR gap of 0.17 to 1.94 over various datasets, including MNIST, X-ray, Glas, and MoNuseg. This highlights our method's significant potential in reconstruction under an uncertain forward model.
Terahertz imaging shows significant potential across diverse fields, yet the cost-effectiveness of multi-pixel imaging equipment remains an obstacle for many researchers. To tackle this issue, the utilization of single-pixel imaging arises as a lower-cost option, however, the data collection process necessary for reconstructing images is time-consuming. Compressive Sensing offers a promising solution by enabling image generation with fewer measurements than required by Nyquist's theorem, yet long processing times remain an issue, especially for large-sized images. Our proposed solution to this issue involves using caustic lens effect induced by perturbations in a ripple tank as a sampling mask. The dynamic characteristics of the ripple tank introduce randomness into the sampling process, thereby reducing measurement time through exploitation of the inherent sparsity of THz band signals. In this study, a Convolutional Neural Network was used to conduct target classification, based on the distinctive signal patterns obtained via the caustic lens mask. The suggested classifier obtained a 95.16 % accuracy rate in differentiating targets resembling Latin letters.
Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal estimation tasks. An important theoretical question, which has only recently received attention, is the development of generalization error bounds for unrolled DNNs. These bounds deliver theoretical and practical insights into the performance of a DNN on empirical datasets that are distinct from, but sampled from, the probability density generating the DNN training data. In this paper, we develop novel generalization error bounds for a class of unrolled DNNs that are informed by a compound Gaussian prior. These compound Gaussian networks have been shown to outperform comparative standard and unfolded deep neural networks in compressive sensing and tomographic imaging problems. The generalization error bound is formulated by bounding the Rademacher complexity of the class of compound Gaussian network estimates with Dudley's integral. Under realistic conditions, we show that, at worst, the generalization error scales $\mathcal{O}(n\sqrt{\ln(n)})$ in the signal dimension and $\mathcal{O}(($Network Size$)^{3/2})$ in network size.
Hyperspectral Imaging (HSI) is used in a wide range of applications such as remote sensing, yet the transmission of the HS images by communication data links becomes challenging due to the large number of spectral bands that the HS images contain together with the limited data bandwidth available in real applications. Compressive Sensing reduces the images by randomly subsampling the spectral bands of each spatial pixel and then it performs the image reconstruction of all the bands using recovery algorithms which impose sparsity in a certain transform domain. Since the image pixels are not strictly sparse, this work studies a data sparsification pre-processing stage prior to compression to ensure the sparsity of the pixels. The sparsified images are compressed $2.5\times$ and then recovered using the Generalized Orthogonal Matching Pursuit algorithm (gOMP) characterized by high accuracy, low computational requirements and fast convergence. The experiments are performed in five conventional hyperspectral images where the effect of different sparsification levels in the quality of the uncompressed as well as the recovered images is studied. It is concluded that the gOMP algorithm reconstructs the hyperspectral images with higher accuracy as well as faster convergence when the pixels are highly sparsified and hence at the expense of reducing the quality of the recovered images with respect to the original images.
Hyperspectral Imaging comprises excessive data consequently leading to significant challenges for data processing, storage and transmission. Compressive Sensing has been used in the field of Hyperspectral Imaging as a technique to compress the large amount of data. This work addresses the recovery of hyperspectral images 2.5x compressed. A comparative study in terms of the accuracy and the performance of the convex FISTA/ADMM in addition to the greedy gOMP/BIHT/CoSaMP recovery algorithms is presented. The results indicate that the algorithms recover successfully the compressed data, yet the gOMP algorithm achieves superior accuracy and faster recovery in comparison to the other algorithms at the expense of high dependence on unknown sparsity level of the data to recover.
Video Captioning (VC) is a challenging multi-modal task since it requires describing the scene in language by understanding various and complex videos. For machines, the traditional VC follows the "imaging-compression-decoding-and-then-captioning" pipeline, where compression is pivot for storage and transmission. However, in such a pipeline, some potential shortcomings are inevitable, i.e., information redundancy resulting in low efficiency and information loss during the sampling process for captioning. To address these problems, in this paper, we propose a novel VC pipeline to generate captions directly from the compressed measurement, which can be captured by a snapshot compressive sensing camera and we dub our model SnapCap. To be more specific, benefiting from the signal simulation, we have access to obtain abundant measurement-video-annotation data pairs for our model. Besides, to better extract language-related visual representations from the compressed measurement, we propose to distill the knowledge from videos via a pre-trained CLIP with plentiful language-vision associations to guide the learning of our SnapCap. To demonstrate the effectiveness of SnapCap, we conduct experiments on two widely-used VC datasets. Both the qualitative and quantitative results verify the superiority of our pipeline over conventional VC pipelines. In particular, compared to the "caption-after-reconstruction" methods, our SnapCap can run at least 3$\times$ faster, and achieve better caption results.
Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation (SE) mechanisms into the ISTA block. This block serves as a deep equilibrium layer, connected to a semi-tensor product network (STP-Net) for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation trade-offs. Additionally, the model benefits from multi-scale dilated convolutions, further enhancing performance.
Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for future wireless systems. In this paper, we develop a novel scheme that utilizes orthogonal frequency division multiplexing (OFDM) pilot signals in ISAC systems to sense the electromagnetic (EM) property of the target and thus also identify the material of the target. Specifically, we first establish an end-to-end EM propagation model by means of Maxwell equations, where the EM property of the target is captured by a closed-form expression of the ISAC channel, incorporating the Lippmann-Schwinger equation and the method of moments (MOM) for discretization. We then model the relative permittivity and conductivity distribution (RPCD) within a specified detection region. Based on the sensing model, we introduce a multi-frequency-based EM property sensing method by which the RPCD can be reconstructed from compressive sensing techniques that exploits the joint sparsity structure of the EM property vector. To improve the sensing accuracy, we design a beamforming strategy from the communications transmitter based on the Born approximation that can minimize the mutual coherence of the sensing matrix. The optimization problem is cast in terms of the Gram matrix and is solved iteratively to obtain the optimal beamforming matrix. Simulation results demonstrate the efficacy of the proposed method in achieving high-quality RPCD reconstruction and accurate material classification. Furthermore, improvements in RPCD reconstruction quality and material classification accuracy are observed with increased signal-to-noise ratio (SNR) or reduced target-transmitter distance.
Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches. The first method developed is an iterative algorithm, called generalized compound Gaussian least squares (G-CG-LS), that minimizes a regularized least squares objective function where the regularization enforces a CG prior. G-CG-LS is then unrolled, or unfolded, to furnish our second method, which is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information. A detailed computational theory on convergence properties of G-CG-LS and thorough numerical experiments for DR-CG-Net are provided. Due to the comprehensive nature of the CG prior, these experiments show that DR-CG-Net outperforms competitive prior art methods in tomographic imaging and compressive sensing, especially in challenging low-training scenarios.
This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an $n \times q$ matrix, $\X^* =[ \x_1^*, \x_2^*, \cdots , \x_q^*]$ from $m$ independent linear projections of each of its $q$ columns, given by $\y_k :=\A_k\x_k^*$, $k \in [q]$. Here, $\y_k$ is an $m$-length vector with $m < n$. We assume that the matrix $\X^*$ can be decomposed as $\X^*=\L^*+\S^*$, where $\L^*$ is a low rank matrix of rank $r << \min(n,q)$ and $\S^*$ is a sparse matrix. Each column of $\S$ contains $\rho$ non-zero entries. The matrices $\A_k$ are known and mutually independent for different $k$. To address this recovery problem, we propose a novel fast GD-based solution called AltGDmin-LR+S, which is memory and communication efficient. We numerically evaluate its performance by conducting a detailed simulation-based study.
Compressive sensing (CS) has been widely applied in signal and image processing fields. Traditional CS reconstruction algorithms have a complete theoretical foundation but suffer from the high computational complexity, while fashionable deep network-based methods can achieve high-accuracy reconstruction of CS but are short of interpretability. These facts motivate us to develop a deep unfolding network named the penalty-based independent parameters optimization network (PIPO-Net) to combine the merits of the above mentioned two kinds of CS methods. Each module of PIPO-Net can be viewed separately as an optimization problem with respective penalty function. The main characteristic of PIPO-Net is that, in each round of training, the learnable parameters in one module are updated independently from those of other modules. This makes the network more flexible to find the optimal solutions of the corresponding problems. Moreover, the mean-subtraction sampling and the high-frequency complementary blocks are developed to improve the performance of PIPO-Net. Experiments on reconstructing CS images demonstrate the effectiveness of the proposed PIPO-Net.
Real--time and accurate construction of regional sound speed profiles (SSP) is important for building underwater positioning, navigation, and timing (PNT) systems as it greatly affect the signal propagation modes such as trajectory. In this paper, we summarizes and analyzes the current research status in the field of underwater SSP construction, and the mainstream methods include direct SSP measurement and SSP inversion. In the direct measurement method, we compare the performance of popular international commercial temperature, conductivity, and depth profilers (CTD). While for the inversion methods, the framework and basic principles of matched field processing (MFP), compressive sensing (CS), and deep learning (DL) for constructing SSP are introduced, and their advantages and disadvantages are compared. The traditional direct measurement method has good accuracy performance, but it usually takes a long time. The proposal of SSP inversion method greatly improves the convenience and real--time performance, but the accuracy is not as good as the direct measurement method. Currently, the SSP inversion relies on sonar observation data, making it difficult to apply to areas that couldn't be covered by underwater observation systems, and these methods are unable to predict the distribution of sound velocity at future times. How to comprehensively utilize multi-source data and provide elastic sound velocity distribution estimation services with different accuracy and real-time requirements for underwater users without sonar observation data is the mainstream trend in future research on SSP construction.
Underwater Sound Speed Profile (SSP) distribution has great influence on the propagation mode of acoustic signal, thus the fast and accurate estimation of SSP is of great importance in building underwater observation systems. The state-of-the-art SSP inversion methods include frameworks of matched field processing (MFP), compressive sensing (CS), and feedforeward neural networks (FNN), among which the FNN shows better real-time performance while maintain the same level of accuracy. However, the training of FNN needs quite a lot historical SSP samples, which is diffcult to be satisfied in many ocean areas. This situation is called few-shot learning. To tackle this issue, we propose a multi-task learning (MTL) model with partial parameter sharing among different traning tasks. By MTL, common features could be extracted, thus accelerating the learning process on given tasks, and reducing the demand for reference samples, so as to enhance the generalization ability in few-shot learning. To verify the feasibility and effectiveness of MTL, a deep-ocean experiment was held in April 2023 at the South China Sea. Results shows that MTL outperforms the state-of-the-art methods in terms of accuracy for SSP inversion, while inherits the real-time advantage of FNN during the inversion stage.
Camera sensors have been widely used in intelligent robotic systems. Developing camera sensors with high sensing efficiency has always been important to reduce the power, memory, and other related resources. Inspired by recent success on programmable sensors and deep optic methods, we design a novel video compressed sensing system with spatially-variant compression ratios, which achieves higher imaging quality than the existing snapshot compressed imaging methods with the same sensing costs. In this article, we also investigate the data transmission methods for programmable sensors, where the performance of communication systems is evaluated by the reconstructed images or videos rather than the transmission of sensor data itself. Usually, different reconstruction algorithms are designed for applications in high dynamic range imaging, video compressive sensing, or motion debluring. This task-aware property inspires a semantic communication framework for programmable sensors. In this work, a policy-gradient based reinforcement learning method is introduced to achieve the explicit trade-off between the compression (or transmission) rate and the image distortion. Numerical results show the superiority of the proposed methods over existing baselines.
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. The main bottleneck involves repeated matrix inversion and log-determinant computation for multiple large covariance matrices. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices. Our approach combines Monte Carlo sampling with iterative linear solvers. Our experiments reveal that compared to the existing baseline, our algorithm can be up to thousands of times faster and an order of magnitude more memory-efficient.
Massive multiple-input multiple-output (MIMO) enjoys great advantage in 5G wireless communication systems owing to its spectrum and energy efficiency. However, hundreds of antennas require large volumes of pilot overhead to guarantee reliable channel estimation in FDD massive MIMO system. Compressive sensing (CS) has been applied for channel estimation by exploiting the inherent sparse structure of massive MIMO channel but suffer from high complexity. To overcome this challenge, this paper develops a hybrid channel estimation scheme by integrating the model-driven CS and data-driven deep unrolling technique. The proposed scheme consists of a coarse estimation part and a fine correction part to respectively exploit the inter- and intraframe sparsities of channels to greatly reduce the pilot overhead. Theoretical result is provided to indicate the convergence of the fine correction and coarse estimation net. Simulation results are provided to verify that our scheme can estimate MIMO channels with low pilot overhead while guaranteeing estimation accuracy with relatively low complexity.
This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and one-dimensional (1D) trajectories derived from the discrete Radon transform (DRT). Unlike radial trajectories, DRT projections can be back-projected without interpolation. Thus, we also propose a novel reconstruction method based on the exact projections of the DRT called finite Fourier reconstruction (FFR). We term this combined p.frac and FFR strategy, finite compressive sensing (FCS), with image recovery demonstrated on experimental and simulated data; image quality comparisons are made with Cartesian random sampling in 1D and two-dimensional (2D), as well as radial under-sampling in a more constrained experiment. Our experiments indicate FCS enables 3-5dB gain in peak signal-to-noise ratio (PSNR) for 2-, 4- and 8-fold under-sampling compared to 1D Cartesian random sampling. This paper aims to: Review common sampling strategies for compressed sensing (CS)-magnetic resonance imaging (MRI) to inform the motivation of a projective and Cartesian sampling scheme. Compare the incoherence of these sampling strategies and the proposed p.frac. Compare reconstruction quality of the sampling schemes under various reconstruction strategies to determine the suitability of p.frac for CS-MRI. It is hypothesised that because p.frac is a highly incoherent sampling scheme, that reconstructions will be of high quality compared to 1D Cartesian phase-encode under-sampling.
We introduce an interpretable deep learning approach for direction of arrival (DOA) estimation with a single snapshot. Classical subspace-based methods like MUSIC and ESPRIT use spatial smoothing on uniform linear arrays for single snapshot DOA estimation but face drawbacks in reduced array aperture and inapplicability to sparse arrays. Single-snapshot methods such as compressive sensing and iterative adaptation approach (IAA) encounter challenges with high computational costs and slow convergence, hampering real-time use. Recent deep learning DOA methods offer promising accuracy and speed. However, the practical deployment of deep networks is hindered by their black-box nature. To address this, we propose a deep-MPDR network translating minimum power distortionless response (MPDR)-type beamformer into deep learning, enhancing generalization and efficiency. Comprehensive experiments conducted using both simulated and real-world datasets substantiate its dominance in terms of inference time and accuracy in comparison to conventional methods. Moreover, it excels in terms of efficiency, generalizability, and interpretability when contrasted with other deep learning DOA estimation networks.