Hagit Messer

Hai Victor Habi, Hagit Messer, Yoram Bresler

The Cramér-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the likelihood of the measurements given the parameters, or equivalently a precise and explicit statistical model for the data. In many applications, such a model is not available. Instead, this work introduces a novel approach to approximate the CRB using data-driven methods, which removes the requirement for an analytical statistical model. This approach is based on the recent success of deep generative models in modeling complex, high-dimensional distributions. Using a learned normalizing flow model, we model the distribution of the measurements and obtain an approximation of the CRB, which we call Generative Cramér-Rao Bound (GCRB). Numerical experiments on simple problems validate this approach, and experiments on two image processing tasks of image denoising and edge detection with a learned camera noise model demonstrate its power and benefits.

Badr Moufad, Albina Ilina, Hai Victor Habi et al.

Commercial Microwave Links (CMLs) offer dense spatial coverage for rainfall sensing but produce path-integrated measurements that make accurate ground-level reconstruction challenging. Existing methods typically oversimplify CMLs as point sensors and neglect line integration relating rainfall to signal attenuation, resulting in degraded performance under heterogeneous precipitation. In this work, we view rain field reconstruction as a Bayesian inverse problem with Diffusion Models (DMs) as high-fidelity spatial priors. We show that diffusion models better preserve key rainfall statistics compared to censored Gaussian processes. Framing rainfall estimation as a Bayesian inverse problem with a DM prior enables training-free posterior sampling using a broad family of methods, including Plug-and-Play, Sequential Monte Carlo, and Replica Exchange methods. Experiments on synthetic and real-world datasets demonstrate consistent improvements over established CML-based reconstruction baselines.

Dror Jacoby, Yanzhi Li, Shuyue Yu et al.

Millimeter-wave (mmWave) links are increasingly utilized in wireless x-haul transport to meet growing service demands. However, the inherent susceptibility of mmWave links to weather-related attenuation creates uncertainty about future network capacity which can significantly affect Quality of Service (QoS). This creates a critical challenge: how to make admission control decisions for slices with QoS requirements, balancing acceptance rewards against the risk of future QoS-violation penalties due to capacity uncertainty? To address this, we develop a proactive slice admission control framework that tightly integrates: (i) a predictor that leverages historical link measurements to forecast short-term attenuation and quantify uncertainty; and (ii) an admission control algorithm that incorporates both the predictions and uncertainties to maximize rewards and minimize QoS-violation penalties. We compare our framework against baseline, state-of-the-art, and idealized oracle algorithms using real-world mmWave x-haul data and residential traffic traces. Simulations suggest that our framework can achieve revenues that are 250% larger than baseline algorithms and 75% larger than state-of-the-art algorithms.

Hai Victor Habi, Hagit Messer, Yoram Bresler

The Bayesian Cramér-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cramér-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise.