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.

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that can guide the reconstruction towards solutions that appear natural. The success of diffusion models over the last few years has made them a leading candidate for this task. However, the sequential nature of diffusion models makes this conditional sampling process challenging. Furthermore, since diffusion models are often defined in the latent space of an autoencoder, the encoder-decoder transformations introduce additional difficulties. To address these challenges, we suggest a novel sampling method based on sequential Monte Carlo (SMC) in the latent space of diffusion models. We name our method LD-SMC. We define a generative model for the data using additional auxiliary observations and perform posterior inference with SMC sampling based on a backward diffusion process. Empirical evaluations on ImageNet and FFHQ show the benefits of LD-SMC over competing methods in various inverse problem tasks and especially in challenging inpainting tasks.

Zero-shot quantization (ZSQ) using synthetic data is a key approach for post-training quantization (PTQ) under privacy and security constraints. However, existing data generation methods often struggle to effectively generate data suitable for hardware-friendly quantization, where all model layers are quantized. We analyze existing data generation methods based on batch normalization (BN) matching and identify several gaps between synthetic and real data: 1) Current generation algorithms do not optimize the entire synthetic dataset simultaneously; 2) Data augmentations applied during training are often overlooked; and 3) A distribution shift occurs in the final model layers due to the absence of BN in those layers. These gaps negatively impact ZSQ performance, particularly in hardware-friendly quantization scenarios. In this work, we propose Data Generation for Hardware-Friendly Quantization (DGH), a novel method that addresses these gaps. DGH jointly optimizes all generated images, regardless of the image set size or GPU memory constraints. To address data augmentation mismatches, DGH includes a preprocessing stage that mimics the augmentation process and enhances image quality by incorporating natural image priors. Finally, we propose a new distribution-stretching loss that aligns the support of the feature map distribution between real and synthetic data. This loss is applied to the model's output and can be adapted to various tasks. DGH demonstrates significant improvements in quantization performance across multiple tasks, achieving up to a 30% increase in accuracy for hardware-friendly ZSQ in both classification and object detection, often performing on par with real data.

We introduce the Generative Barankin Bound (GBB), a learned Barankin Bound, for evaluating the achievable performance in estimating the direction of arrival (DOA) of a source in non-asymptotic conditions, when the statistics of the measurement are unknown. We first learn the measurement distribution using a conditional normalizing flow (CNF) and then use it to derive the GBB. We show that the resulting learned bound approximates the analytical Barankin bound well for the case of a Gaussian signal in Gaussian noise, Then, we evaluate the GBB for cases where analytical expressions for the Barankin Bound cannot be derived. In particular, we study the effect of non-Gaussian scenarios on the threshold SNR.

The Misspecified Cramér-Rao lower bound (MCRB) provides a lower bound on the performance of any unbiased estimator of parameter vector θ under model misspecification. An approximation of the MCRB can be numerically evaluated using a set of i.i.d samples of the true distribution at θ. However, obtaining a good approximation for multiple values of θ requires collocating an unrealistically large number of samples. In this paper, we present a method for approximating the MCRB using a Generative Model, referred to as a Generative Misspecified Lower Bound (GMLB), in which we train a generative model on data from the true measurement distribution. Then, the generative model can generate as many samples as required for any θ, and therefore the GMLB can use a limited set of training data to achieve an excellent approximation of the MCRB for any parameter. We demonstrate the GMLB on two examples: a misspecified Linear Gaussian model; and a Non-Linear Truncated Gaussian model. In both cases, we empirically show the benefits of the GMLB in accuracy and sample complexity. In addition, we show the ability of the GMLB to approximate the MCRB on unseen parameters.

The use of recurrent neural networks (RNNs) to utilize measurements from commercial microwave links (CMLs) has recently gained attention. Whereas previous studies focused on the performance of methods for wet-dry classification, here we propose an RNN algorithm for estimating the rain-rate. We empirically analyzed the proposed algorithm, using real data, and compared it with the traditional power-law (PL)-based algorithm, commonly used for estimating rain from CML attenuation measurements. Our analysis shows that the data-driven RNN algorithm, when properly trained, outperforms the PL algorithm in terms of accuracy. On the other hand, the PL algorithm is simpler and more robust when dealing with a large variety of corruptions and adverse conditions. We then introduced a time normalization (TN) layer for controlling the trade-off between performance and robustness of the RNN methods, and demonstrated its performance.

A Power-Law relation between attenuation and rain rate has proven to be a useful tool in wireless network design at microwave and mmWave frequencies. In the last decade this relation has also been used for estimating rain from signal level measurements in Commercial Microwave Links (CMLs). In this paper we empirically show that while the power-law relation provides good approximation for relating attenuation and rain-rate in terrestrial microwave links of length 1-20Km, for links shorter than 1km, widely used in 5G technologies, it shows significant errors. We then suggest a recurrent neural network (RNN) approach to relate attenuation with rain rate and we show that it overcomes the uncertainties in short links.