Beyond their impressive sampling capabilities, score-based diffusion models offer a powerful analysis tool in the form of unbiased density estimation of a query sample under the training data distribution. In this work, we investigate the robustness of density estimation using the probability flow (PF) neural ordinary differential equation (ODE) model against gradient-based likelihood maximization attacks and the relation to sample complexity, where the compressed size of a sample is used as a measure of its complexity. We introduce and evaluate six gradient-based log-likelihood maximization attacks, including a novel reverse integration attack. Our experimental evaluations on CIFAR-10 show that density estimation using the PF ODE is robust against high-complexity, high-likelihood attacks, and that in some cases adversarial samples are semantically meaningful, as expected from a robust estimator.
We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.
Automotive radar has increasingly attracted attention due to growing interest in autonomous driving technologies. Acquiring situational awareness using multimodal data collected at high sampling rates by various sensing devices including cameras, LiDAR, and radar requires considerable power, memory and compute resources which are often limited at an edge device. In this paper, we present a novel adaptive radar sub-sampling algorithm designed to identify regions that require more detailed/accurate reconstruction based on prior environmental conditions' knowledge, enabling near-optimal performance at considerably lower effective sampling rates. Designed to robustly perform under variable weather conditions, the algorithm was shown on the Oxford raw radar and RADIATE dataset to achieve accurate reconstruction utilizing only 10% of the original samples in good weather and 20% in extreme (snow, fog) weather conditions. A further modification of the algorithm incorporates object motion to enable reliable identification of important regions. This includes monitoring possible future occlusions caused by objects detected in the present frame. Finally, we train a YOLO network on the RADIATE dataset to perform object detection directly on RADAR data and obtain a 6.6% AP50 improvement over the baseline Faster R-CNN network.
Channel estimation is a critical task in multiple-input multiple-output digital communications that has effects on end-to-end system performance. In this work, we introduce a novel approach for channel estimation using deep score-based generative models. These models are trained to estimate the gradient of the log-prior distribution, and can be used to iteratively refine estimates, given observed measurements of a signal. We introduce a framework for training score-based generative models for wireless channels, as well as performing channel estimation using posterior sampling at test time. We derive theoretical robustness guarantees of channel estimation with posterior sampling in single-input single-output scenarios, and show that the observations regarding estimation performance are verified experimentally in MIMO channels. Our results in simulated clustered delay line channels show competitive in-distribution performance without error floors in the high signal-to-noise ratio regime, and robust out-of-distribution performance, outperforming competing deep learning methods by up to 5 dB in end-to-end communication performance, while the complexity analysis reveals how model architecture can efficiently trade performance for estimation latency.
Robust and accurate sensing is of critical importance for advancing autonomous automotive systems. The need to acquire situational awareness in complex urban conditions using sensors such as radar has motivated research on power and latency-efficient signal acquisition methods. In this paper, we present an end-to-end signal processing pipeline, capable of operating in extreme weather conditions, that relies on sub-sampled radar data to perform object detection in vehicular settings. The results of the object detection are further utilized to sub-sample forthcoming radar data, which stands in contrast to prior work where the sub-sampling relies on image information. We show robust detection based on radar data reconstructed using 20% of samples under extreme weather conditions such as snow or fog, and on low-illuminated nights. Additionally, we generate 20% sampled radar data in a fine-tuning set and show 1.1% gain in AP50 across scenes and 3% AP50 gain in motorway condition.
Channel estimation is a critical task in digital communications that greatly impacts end-to-end system performance. In this work, we introduce a novel approach for multiple-input multiple-output (MIMO) channel estimation using deep diffusion models. Our method uses a deep neural network that is trained to estimate the gradient of the log-likelihood of wireless channels at any point in high-dimensional space, and leverages this model to solve channel estimation via posterior sampling. We train a deep diffusion model on channel realizations from the CDL-D model for two antenna spacings and show that the approach leads to competitive in- and out-of-distribution performance when compared to generative adversarial network (GAN) and compressed sensing (CS) methods. When tested on CDL-C channels which are never seen during training or fine-tuned on, our approach leads to end-to-end coded performance gains of up to $3$ dB compared to CS methods and losses of only $0.5$ dB compared to ideal channel knowledge. To encourage open and reproducible research, our source code is available at https://github.com/utcsilab/diffusion-channels .
Deep learning has been recently applied to physical layer processing in digital communication systems in order to improve end-to-end performance. In this work, we introduce a novel deep learning solution for soft bit quantization across wideband channels. Our method is trained end-to-end with quantization- and entropy-aware augmentations to the loss function and is used at inference in conjunction with source coding to achieve near-optimal compression gains over wideband channels. To efficiently train our method, we prove and verify that a fixed feature space quantization scheme is sufficient for efficient learning. When tested on channel distributions never seen during training, the proposed method achieves a compression gain of up to $10 \%$ in the high SNR regime versus previous state-of-the-art methods. To encourage reproducible research, our implementation is publicly available at https://github.com/utcsilab/wideband-llr-deep.
The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for example, human faces and MNIST digits), and it is known to perform poorly on out-of-distribution samples. In this paper, we present the first successful application of the CSGM framework on clinical MRI data. We train a generative prior on brain scans from the fastMRI dataset, and show that posterior sampling via Langevin dynamics achieves high quality reconstructions. Furthermore, our experiments and theory show that posterior sampling is robust to changes in the ground-truth distribution and measurement process. Our code and models are available at: \url{https://github.com/utcsilab/csgm-mri-langevin}.
Accelerated multi-coil magnetic resonance imaging reconstruction has seen a substantial recent improvement combining compressed sensing with deep learning. However, most of these methods rely on estimates of the coil sensitivity profiles, or on calibration data for estimating model parameters. Prior work has shown that these methods degrade in performance when the quality of these estimators are poor or when the scan parameters differ from the training conditions. Here we introduce Deep J-Sense as a deep learning approach that builds on unrolled alternating minimization and increases robustness: our algorithm refines both the magnetization (image) kernel and the coil sensitivity maps. Experimental results on a subset of the knee fastMRI dataset show that this increases reconstruction performance and provides a significant degree of robustness to varying acceleration factors and calibration region sizes.