Physics Embedded Machine Learning for Electromagnetic Data Imaging

Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML) techniques and especially deep learning (DL) show potential in fast and accurate imaging. However, the high performance of purely data-driven approaches relies on constructing a training set that is statistically consistent with practical scenarios, which is often not possible in EM imaging tasks. Consequently, generalizability becomes a major concern. On the other hand, physical principles underlie EM phenomena and provide baselines for current imaging techniques. To benefit from prior knowledge in big data and the theoretical constraint of physical laws, physics embedded ML methods for EM imaging have become the focus of a large body of recent work. This article surveys various schemes to incorporate physics in learning-based EM imaging. We first introduce background on EM imaging and basic formulations of the inverse problem. We then focus on three types of strategies combining physics and ML for linear and nonlinear imaging and discuss their advantages and limitations. Finally, we conclude with open challenges and possible ways forward in this fast-developing field. Our aim is to facilitate the study of intelligent EM imaging methods that will be efficient, interpretable and controllable.

Neural Greedy Pursuit for Feature Selection

We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural networks as predictors in the algorithm to compute the loss and hence, we refer to our method as neural greedy pursuit (NGP). NGP is efficient in selecting $N$ features when $N \ll P$, and it provides a notion of feature importance in a descending order following the sequential selection procedure. We experimentally show that NGP provides better performance than several feature selection methods such as DeepLIFT and Drop-one-out loss. In addition, we experimentally show a phase transition behavior in which perfect selection of all $N$ features without false positives is possible when the training data size exceeds a threshold.

Modulo Sampling of FRI Signals

The dynamic range of an analog-to-digital converter (ADC) is critical during sampling of analog signals. A modulo operation prior to sampling can be used to enhance the effective dynamic range of the ADC. Further, sampling rate of ADC too plays a crucial role and it is desirable to reduce it. Finite-rate-of-innovation (FRI) signal model, which is ubiquitous in many applications, can be used to reduce the sampling rate. In the context of modulo folding for FRI sampling, existing works operate at a very high sampling rate compared to the rate of innovation (RoI) and require a large number of samples compared to the degrees of freedom (DoF) of the FRI signal. Moreover, these approaches use infinite length filters that are practically infeasible. We consider the FRI sampling problem with a compactly supported kernel under the modulo framework. We derive theoretical guarantees and show that FRI signals could be uniquely identified by sampling above the RoI. The number of samples for identifiability is equal to the DoF. We propose a practical algorithm to estimate the FRI parameters from the modulo samples. We show that the proposed approach has the lowest error in estimating the FRI parameters while operating with the lowest number of samples and sampling rates compared to existing techniques. The results are helpful in designing cost-effective, high-dynamic-range ADCs for FRI signals.

Intelligent Reflecting Surface Enabled Sensing: Cramér-Rao Bound Optimization

This paper investigates intelligent reflecting surface (IRS) enabled non-line-of-sight (NLoS) wireless sensing, in which an IRS is dedicatedly deployed to assist an access point (AP) to sense a target at its NLoS region. It is assumed that the AP is equipped with multiple antennas and the IRS is equipped with a uniform linear array. We consider two types of target models, namely the point and extended targets, for which the AP aims to estimate the target's direction-of-arrival (DoA) and the target response matrix with respect to the IRS, respectively, based on the echo signals from the AP-IRS-target-IRS-AP link. Under this setup, we jointly design the transmit beamforming at the AP and the reflective beamforming at the IRS to minimize the Cram\'er-Rao bound (CRB) on the estimation error. Towards this end, we first obtain the CRB expressions for the two target models in closed form. It is shown that in the point target case, the CRB for estimating the DoA depends on both the transmit and reflective beamformers; while in the extended target case, the CRB for estimating the target response matrix only depends on the transmit beamformers. Next, for the point target case, we optimize the joint beamforming design to minimize the CRB, via alternating optimization, semi-definite relaxation, and successive convex approximation. For the extended target case, we obtain the optimal transmit beamforming solution to minimize the CRB in closed form. Finally, numerical results show that for both cases, the proposed designs based on CRB minimization achieve improved sensing performance in terms of mean squared error, as compared to other traditional schemes.

BiTAT: Neural Network Binarization with Task-dependent Aggregated Transformation

Neural network quantization aims to transform high-precision weights and activations of a given neural network into low-precision weights/activations for reduced memory usage and computation, while preserving the performance of the original model. However, extreme quantization (1-bit weight/1-bit activations) of compactly-designed backbone architectures (e.g., MobileNets) often used for edge-device deployments results in severe performance degeneration. This paper proposes a novel Quantization-Aware Training (QAT) method that can effectively alleviate performance degeneration even with extreme quantization by focusing on the inter-weight dependencies, between the weights within each layer and across consecutive layers. To minimize the quantization impact of each weight on others, we perform an orthonormal transformation of the weights at each layer by training an input-dependent correlation matrix and importance vector, such that each weight is disentangled from the others. Then, we quantize the weights based on their importance to minimize the loss of the information from the original weights/activations. We further perform progressive layer-wise quantization from the bottom layer to the top, so that quantization at each layer reflects the quantized distributions of weights and activations at previous layers. We validate the effectiveness of our method on various benchmark datasets against strong neural quantization baselines, demonstrating that it alleviates the performance degeneration on ImageNet and successfully preserves the full-precision model performance on CIFAR-100 with compact backbone networks.

Task-Oriented Sensing, Computation, and Communication Integration for Multi-Device Edge AI

This paper studies a new multi-device edge artificial-intelligent (AI) system, which jointly exploits the AI model split inference and integrated sensing and communication (ISAC) to enable low-latency intelligent services at the network edge. In this system, multiple ISAC devices perform radar sensing to obtain multi-view data, and then offload the quantized version of extracted features to a centralized edge server, which conducts model inference based on the cascaded feature vectors. Under this setup and by considering classification tasks, we measure the inference accuracy by adopting an approximate but tractable metric, namely discriminant gain, which is defined as the distance of two classes in the Euclidean feature space under normalized covariance. To maximize the discriminant gain, we first quantify the influence of the sensing, computation, and communication processes on it with a derived closed-form expression. Then, an end-to-end task-oriented resource management approach is developed by integrating the three processes into a joint design. This integrated sensing, computation, and communication (ISCC) design approach, however, leads to a challenging non-convex optimization problem, due to the complicated form of discriminant gain and the device heterogeneity in terms of channel gain, quantization level, and generated feature subsets. Remarkably, the considered non-convex problem can be optimally solved based on the sum-of-ratios method. This gives the optimal ISCC scheme, that jointly determines the transmit power and time allocation at multiple devices for sensing and communication, as well as their quantization bits allocation for computation distortion control. By using human motions recognition as a concrete AI inference task, extensive experiments are conducted to verify the performance of our derived optimal ISCC scheme.

Robust Unlimited Sampling Beyond Modulo

Analog to digital converters (ADCs) act as a bridge between the analog and digital domains. Two important attributes of any ADC are sampling rate and its dynamic range. For bandlimited signals, the sampling should be above the Nyquist rate. It is also desired that the signals' dynamic range should be within that of the ADC's; otherwise, the signal will be clipped. Nonlinear operators such as modulo or companding can be used prior to sampling to avoid clipping. To recover the true signal from the samples of the nonlinear operator, either high sampling rates are required or strict constraints on the nonlinear operations are imposed, both of which are not desirable in practice. In this paper, we propose a generalized flexible nonlinear operator which is sampling efficient. Moreover, by carefully choosing its parameters, clipping, modulo, and companding can be seen as special cases of it. We show that bandlimited signals are uniquely identified from the nonlinear samples of the proposed operator when sampled above the Nyquist rate. Furthermore, we propose a robust algorithm to recover the true signal from the nonlinear samples. We show that our algorithm has the lowest mean-squared error while recovering the signal for a given sampling rate, noise level, and dynamic range of the compared to existing algorithms. Our results lead to less constrained hardware design to address the dynamic range issues while operating at the lowest rate possible.

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

Beamforming in Integrated Sensing and Communication Systems with Reconfigurable Intelligent Surfaces

We consider transmit beamforming and reflection pattern design in reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC) systems to jointly precode communication symbols and radar waveforms. We treat two settings of multiple users and targets. In the first, we use a single RIS to enhance the communication performance of the ISAC system and design beams with good cross-correlation properties to match a desired beam pattern while guaranteeing a desired signal-to-interference plus noise ratio (SINR) for each user. In the second setting, we use two dedicated RISs to aid the ISAC system, wherein the beams are designed to maximize the worst-case target illumination power while guaranteeing a desired SINR for each user. We propose solvers based on alternating optimization as the design problems in both cases are non-convex optimization problems. Through a number of numerical simulations, we demonstrate the advantages of RIS-assisted ISAC systems. In particular, we show that the proposed single-RIS assisted ISAC system improves the minimum user SINR while suffering from a moderate loss in radar target illumination power. On the other hand, the dual-RIS assisted ISAC system improves both minimum user SINR as well as worst-case target illumination power at the targets, especially when the users and targets are not directly visible.

Mixed-Timescale Deep-Unfolding for Joint Channel Estimation and Hybrid Beamforming

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.