Channel estimation is a critical task in multiple-input multiple-output (MIMO) digital communications that substantially effects end-to-end system performance. In this work, we introduce a novel approach for channel estimation using deep score-based generative models. A model is trained to estimate the gradient of the logarithm of a distribution and is used to iteratively refine estimates given measurements of a signal. We introduce a framework for training score-based generative models for wireless MIMO channels and performing channel estimation based on posterior sampling at test time. We derive theoretical robustness guarantees for channel estimation with posterior sampling in single-input single-output scenarios, and experimentally verify performance in the MIMO setting. Our results in simulated channels show competitive in-distribution performance, and robust out-of-distribution performance, with gains of up to 5 dB in end-to-end coded communication performance compared to supervised deep learning methods. Simulations on the number of pilots show that high fidelity channel estimation with 25% pilot density is possible for MIMO channel sizes of up to 64 × 256. Complexity analysis reveals that model size can efficiently trade performance for estimation latency, and that the proposed approach is competitive with compressed sensing in terms of floating-point operation (FLOP) count.

Significance: Public databases are an important resource for machine learning research, but their growing availability sometimes leads to “off-label” usage, where data published for one task are used for another. This work reveals that such off-label usage could lead to biased, overly optimistic results of machine-learning algorithms. The underlying cause is that public data are processed with hidden processing pipelines that alter the data features. Here we study three well-known algorithms developed for image reconstruction from magnetic resonance imaging measurements and show they could produce biased results with up to 48% artificial improvement when applied to public databases. We relate to the publication of such results as implicit “data crimes” to raise community awareness of this growing big data problem.

Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical physics-based reconstructions. Termed physics-based networks, they incorporate both the known physics of the system via its forward model, and the power of deep learning via data-driven training. However, for realistic large-scale physics-based networks, computing gradients via backpropagation is infeasible due to the memory limitations of graphics processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable physics-based learning for large-scale computational imaging systems. We demonstrate our method on a compressed sensing example, as well as two large-scale real-world systems: 3D multi-channel magnetic resonance imaging and super-resolution optical microscopy.

Purpose: The aim of this work is to develop a method to solve the ill‐posed inverse problem of accelerated image reconstruction while correcting forward model imperfections in the context of subject motion during MRI examinations.Methods: The proposed solution uses a Bayesian framework based on deep generative diffusion models to jointly estimate a motion‐free image and rigid motion estimates from subsampled and motion‐corrupt two‐dimensional (2D) k‐space data.Results: We demonstrate the ability to reconstruct motion‐free images from accelerated two‐dimensional (2D) Cartesian and non‐Cartesian scans without any external reference signal. We show that our method improves over existing correction techniques on both simulated and prospectively accelerated data.Conclusion: We propose a flexible framework for retrospective motion correction of accelerated MRI based on deep generative diffusion models, with potential application to other forward model corruptions.

Image reconstruction is the process of recovering an image from raw, under-sampled signal measurements, and is a critical step in diagnostic medical imaging, such as magnetic resonance imaging (MRI). Recently, data-driven methods have led to improved image quality in MRI reconstruction using a limited number of measurements, but these methods typically rely on the existence of a large, centralized database of fully sampled scans for training. In this work, we investigate federated learning for MRI reconstruction using end-to-end unrolled deep learning models as a means of training global models across multiple clients (data sites), while keeping individual scans local. We empirically identify a low-data regime across a large number of heterogeneous scans, where a small number of training samples per client are available and non-collaborative models lead to performance drops. In this regime, we investigate the performance of adaptive federated optimization algorithms as a function of client data distribution and communication budget. Experimental results show that adaptive optimization algorithms are well suited for the federated learning of unrolled models, even in a limited-data regime (50 slices per data site), and that client-sided personalization can improve reconstruction quality for clients that did not participate in training.