Ruud J. G. van Sloun

Dor H. Shmuel, Julian P. Merkofer, Guy Revach et al. · eth-zurich

Direction of arrival (DoA) estimation is a fundamental task in array processing. A popular family of DoA estimation algorithms are subspace methods, which operate by dividing the measurements into distinct signal and noise subspaces. Subspace methods, such as Multiple Signal Classification (MUSIC) and Root-MUSIC, rely on several restrictive assumptions, including narrowband non-coherent sources and fully calibrated arrays, and their performance is considerably degraded when these do not hold. In this work we propose SubspaceNet; a data-driven DoA estimator which learns how to divide the observations into distinguishable subspaces. This is achieved by utilizing a dedicated deep neural network to learn the empirical autocorrelation of the input, by training it as part of the Root-MUSIC method, leveraging the inherent differentiability of this specific DoA estimator, while removing the need to provide a ground-truth decomposable autocorrelation matrix. Once trained, the resulting SubspaceNet serves as a universal surrogate covariance estimator that can be applied in combination with any subspace-based DoA estimation method, allowing its successful application in challenging setups. SubspaceNet is shown to enable various DoA estimation algorithms to cope with coherent sources, wideband signals, low SNR, array mismatches, and limited snapshots, while preserving the interpretability and the suitability of classic subspace methods.

Noam Koren, Ralf J. J. Mackenbach, Ruud J. G. van Sloun et al.

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as- sumptions about the structure of the kernel integral opera- tor, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular func- tions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high de- gree of expressivity. Furthermore, due to its low-rank struc- ture the computational complexity of applying the operator remains reasonable, leading to a practical system. In exten- sive evaluations on five diverse benchmark equations, SVD- NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable. The code of this work is publicly available at https://github.com/2noamk/SVDNO.git.

Iris A. M. Huijben, Arthur A. Nijdam, Sebastiaan Overeem et al.

Continuous monitoring with an ever-increasing number of sensors has become ubiquitous across many application domains. However, acquired time series are typically high-dimensional and difficult to interpret. Expressive deep learning (DL) models have gained popularity for dimensionality reduction, but the resulting latent space often remains difficult to interpret. In this work we propose SOM-CPC, a model that visualizes data in an organized 2D manifold, while preserving higher-dimensional information. We address a largely unexplored and challenging set of scenarios comprising high-rate time series, and show on both synthetic and real-life data (physiological data and audio recordings) that SOM-CPC outperforms strong baselines like DL-based feature extraction, followed by conventional dimensionality reduction techniques, and models that jointly optimize a DL model and a Self-Organizing Map (SOM). SOM-CPC has great potential to acquire a better understanding of latent patterns in high-rate data streams.

Ben Luijten, Nishith Chennakeshava, Yonina C. Eldar et al.

Medical ultrasound imaging relies heavily on high-quality signal processing to provide reliable and interpretable image reconstructions. Conventionally, reconstruction algorithms where derived from physical principles. These algorithms rely on assumptions and approximations of the underlying measurement model, limiting image quality in settings were these assumptions break down. Conversely, more sophisticated solutions based on statistical modelling, careful parameter tuning, or through increased model complexity, can be sensitive to different environments. Recently, deep learning based methods, which are optimized in a data-driven fashion, have gained popularity. These model-agnostic techniques often rely on generic model structures, and require vast training data to converge to a robust solution. A relatively new paradigm combines the power of the two: leveraging data-driven deep learning, as well as exploiting domain knowledge. These model-based solutions yield high robustness, and require less parameters and training data than conventional neural networks. In this work we provide an overview of these techniques from recent literature, and discuss a wide variety of ultrasound applications. We aim to inspire the reader to further research in this area, and to address the opportunities within the field of ultrasound signal processing. We conclude with a future perspective on model-based deep learning techniques for medical ultrasound.

Hans van Gorp, Merel M. van Gilst, Pedro Fonseca et al.

Gold-standard sleep scoring is based on epoch-based assignment of sleep stages based on a combination of EEG, EOG and EMG signals. However, a polysomnographic recording consists of many other signals that could be used for sleep staging, including cardio-respiratory modalities. Leveraging this signal variety would offer important advantages, for example increasing reliability, resilience to signal loss, and application to long-term non-obtrusive recordings. We developed a deep generative model for automatic sleep staging from a plurality of sensors and any -- arbitrary -- combination thereof. We trained a score-based diffusion model using a dataset of 1947 expert-labelled overnight recordings with 36 different signals, and achieved zero-shot inference on any sensor set by leveraging a novel Bayesian factorization of the score function across the sensors. On single-channel EEG, the model reaches the performance limit in terms of polysomnography inter-rater agreement (5-class accuracy 85.6%, Cohen's kappa 0.791). Moreover, the method offers full flexibility to use any sensor set, for example finger photoplethysmography, nasal flow and thoracic respiratory movements, (5-class accuracy 79.0%, Cohen's kappa of 0.697), or even derivations very unconventional for sleep staging, such as tibialis and sternocleidomastoid EMG (5-class accuracy 71.0%, kappa 0.575). Additionally, we propose a novel interpretability metric in terms of information gain per sensor and show this is linearly correlated with classification performance. Finally, our model allows for post-hoc addition of entirely new sensor modalities by merely training a score estimator on the novel input instead of having to retrain from scratch on all inputs.

M. M. Amaan Valiuddin, Christiaan G. A. Viviers, Ruud J. G. van Sloun et al.

Melanoma is a serious form of skin cancer with high mortality rate at later stages. Fortunately, when detected early, the prognosis of melanoma is promising and malignant melanoma incidence rates are relatively low. As a result, datasets are heavily imbalanced which complicates training current state-of-the-art supervised classification AI models. We propose to use generative models to learn the benign data distribution and detect Out-of-Distribution (OOD) malignant images through density estimation. Normalizing Flows (NFs) are ideal candidates for OOD detection due to their ability to compute exact likelihoods. Nevertheless, their inductive biases towards apparent graphical features rather than semantic context hamper accurate OOD detection. In this work, we aim at using these biases with domain-level knowledge of melanoma, to improve likelihood-based OOD detection of malignant images. Our encouraging results demonstrate potential for OOD detection of melanoma using NFs. We achieve a 9% increase in Area Under Curve of the Receiver Operating Characteristics by using wavelet-based NFs. This model requires significantly less parameters for inference making it more applicable on edge devices. The proposed methodology can aid medical experts with diagnosis of skin-cancer patients and continuously increase survival rates. Furthermore, this research paves the way for other areas in oncology with similar data imbalance issues.

Tristan S. W. Stevens, Hans van Gorp, Faik C. Meral et al.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Julian P. Merkofer, Dennis M. J. van de Sande, Sina Amirrajab et al.

This work proposes a method to accelerate the acquisition of high-quality edited magnetic resonance spectroscopy (MRS) scans using machine learning models taking the sample covariance matrix as input. The method is invariant to the number of transients and robust to noisy input data for both synthetic as well as in-vivo scenarios.

Tristan S. W. Stevens, Oisín Nolan, Jean-Luc Robert et al.

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25$\times$, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8\% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.

M. M. Amaan Valiuddin, Christiaan G. A. Viviers, Ruud J. G. van Sloun et al.

Data uncertainties, such as sensor noise, occlusions or limitations in the acquisition method can introduce irreducible ambiguities in images, which result in varying, yet plausible, semantic hypotheses. In Machine Learning, this ambiguity is commonly referred to as aleatoric uncertainty. In image segmentation, latent density models can be utilized to address this problem. The most popular approach is the Probabilistic U-Net (PU-Net), which uses latent Normal densities to optimize the conditional data log-likelihood Evidence Lower Bound. In this work, we demonstrate that the PU-Net latent space is severely sparse and heavily under-utilized. To address this, we introduce mutual information maximization and entropy-regularized Sinkhorn Divergence in the latent space to promote homogeneity across all latent dimensions, effectively improving gradient-descent updates and latent space informativeness. Our results show that by applying this on public datasets of various clinical segmentation problems, our proposed methodology receives up to 11% performance gains compared against preceding latent variable models for probabilistic segmentation on the Hungarian-Matched Intersection over Union. The results indicate that encouraging a homogeneous latent space significantly improves latent density modeling for medical image segmentation.

Simon W. Penninga, Ruud J. G. van Sloun

In this paper we propose the Iterative Amortized Hierarchical Variational Autoencoder (IA-HVAE), which expands on amortized inference with a hybrid scheme containing an initial amortized guess and iterative refinement with decoder gradients. We achieve this by creating a linearly separable decoder in a transform domain (e.g. Fourier space), enabling real-time applications with very high model depths. The architectural change leads to a 35x speed-up for iterative inference with respect to the traditional HVAE. We show that our hybrid approach outperforms fully amortized and fully iterative equivalents in accuracy and speed respectively. Moreover, the IAHVAE shows improved reconstruction quality over a vanilla HVAE in inverse problems such as deblurring and denoising.

Oisin Nolan, Tristan S. W. Stevens, Wessel L. van Nierop et al.

Subsampling is commonly used to mitigate costs associated with data acquisition, such as time or energy requirements, motivating the development of algorithms for estimating the fully-sampled signal of interest $x$ from partially observed measurements $y$. In maximum entropy sampling, one selects measurement locations that are expected to have the highest entropy, so as to minimize uncertainty about $x$. This approach relies on an accurate model of the posterior distribution over future measurements, given the measurements observed so far. Recently, diffusion models have been shown to produce high-quality posterior samples of high-dimensional signals using guided diffusion. In this work, we propose Active Diffusion Subsampling (ADS), a method for designing intelligent subsampling masks using guided diffusion in which the model tracks a distribution of beliefs over the true state of $x$ throughout the reverse diffusion process, progressively decreasing its uncertainty by actively choosing to acquire measurements with maximum expected entropy, ultimately producing the posterior distribution $p(x \mid y)$. ADS can be applied using pre-trained diffusion models for any subsampling rate, and does not require task-specific retraining - just the specification of a measurement model. Furthermore, the maximum entropy sampling policy employed by ADS is interpretable, enhancing transparency relative to existing methods using black-box policies. Code is available at https://active-diffusion-subsampling.github.io/.

Ruud JG van Sloun

Ultrasound (US) has the unique potential to offer access to medical imaging to anyone, everywhere. Devices have become ultra-portable and cost-effective, akin to the stethoscope. Nevertheless US image quality and diagnostic efficacy are still highly operator- and patient-dependent. In difficult-to-image patients, image quality is often insufficient for reliable diagnosis. In this paper, we put forth that US imaging systems can be recast as information-seeking agents that engage in reciprocal interactions with their anatomical environment. Such agents autonomously adapt their transmit-receive sequences to fully personalize imaging and actively maximize information gain in-situ. To that end, we will show that the sequence of pulse-echo experiments that a US system performs can be interpreted as a perception-action loop: the action is the data acquisition, probing tissue with acoustic waves and recording reflections at the detection array, and perception is the inference of the anatomical and or functional state, potentially including associated diagnostic quantities. We then equip systems with a mechanism to actively reduce uncertainty and maximize diagnostic value across a sequence of experiments, treating action and perception jointly using Bayesian inference given generative models of the environment and action-conditional pulse-echo observations. Since the representation capacity of the generative models dictates both the quality of inferred anatomical states and the effectiveness of inferred sequences of future imaging actions, we will be greatly leveraging the enormous advances in deep generative modelling that are currently disrupting many fields and society at large. Finally, we show some examples of cognitive, closed-loop, US systems that perform active beamsteering and adaptive scanline selection, based on deep generative models that track anatomical belief states.

Ivana Nikoloska, Hamdi Joudeh, Ruud van Sloun et al.

Quantum sensing exploits non-classical effects to overcome limitations of classical sensors, with applications ranging from gravitational-wave detection to nanoscale imaging. However, practical quantum sensors built on noisy intermediate-scale quantum (NISQ) devices face significant noise and sampling constraints, and current variational quantum sensing (VQS) methods lack rigorous performance guarantees. This paper proposes an online control framework for VQS that dynamically updates the variational parameters while providing deterministic error bars on the estimates. By leveraging online conformal inference techniques, the approach produces sequential estimation sets with a guaranteed long-term risk level. Experiments on a quantum magnetometry task confirm that the proposed dynamic VQS approach maintains the required reliability over time, while still yielding precise estimates. The results demonstrate the practical benefits of combining variational quantum algorithms with online conformal inference to achieve reliable quantum sensing on NISQ devices.

Tristan S. W. Stevens, Oisín Nolan, Oudom Somphone et al.

Three-dimensional ultrasound enables real-time volumetric visualization of anatomical structures. Unlike traditional 2D ultrasound, 3D imaging reduces the reliance on precise probe orientation, potentially making ultrasound more accessible to clinicians with varying levels of experience and improving automated measurements and post-exam analysis. However, achieving both high volume rates and high image quality remains a significant challenge. While 3D diverging waves can provide high volume rates, they suffer from limited tissue harmonic generation and increased multipath effects, which degrade image quality. One compromise is to retain the focusing in elevation while leveraging unfocused diverging waves in the lateral direction to reduce the number of transmissions per elevation plane. Reaching the volume rates achieved by full 3D diverging waves, however, requires dramatically undersampling the number of elevation planes. Subsequently, to render the full volume, simple interpolation techniques are applied. This paper introduces a novel approach to 3D ultrasound reconstruction from a reduced set of elevation planes by employing diffusion models (DMs) to achieve increased spatial and temporal resolution. We compare both traditional and supervised deep learning-based interpolation methods on a 3D cardiac ultrasound dataset. Our results show that DM-based reconstruction consistently outperforms the baselines in image quality and downstream task performance. Additionally, we accelerate inference by leveraging the temporal consistency inherent to ultrasound sequences. Finally, we explore the robustness of the proposed method by exploiting the probabilistic nature of diffusion posterior sampling to quantify reconstruction uncertainty and demonstrate improved recall on out-of-distribution data with synthetic anomalies under strong subsampling.

Wessel L. van Nierop, Nir Shlezinger, Ruud J. G. van Sloun

Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a differentiable particle filter that leverages the unsupervised variational SMC objective to parameterize the proposal and transition distributions with a neural network, designed to learn from high-dimensional observations. Experimental results demonstrate that our approach outperforms established baselines in tracking the challenging Lorenz attractor from high-dimensional and partial observations. Furthermore, an evidence lower bound based evaluation indicates that our method offers a more accurate representation of the posterior distribution.

Simon W. Penninga, Hans van Gorp, Ruud J. G. van Sloun

Ultrasound images are commonly formed by sequential acquisition of beam-steered scan-lines. Minimizing the number of required scan-lines can significantly enhance frame rate, field of view, energy efficiency, and data transfer speeds. Existing approaches typically use static subsampling schemes in combination with sparsity-based or, more recently, deep-learning-based recovery. In this work, we introduce an adaptive subsampling method that maximizes intrinsic information gain in-situ, employing a Sylvester Normalizing Flow encoder to infer an approximate Bayesian posterior under partial observation in real-time. Using the Bayesian posterior and a deep generative model for future observations, we determine the subsampling scheme that maximizes the mutual information between the subsampled observations, and the next frame of the video. We evaluate our approach using the EchoNet cardiac ultrasound video dataset and demonstrate that our active sampling method outperforms competitive baselines, including uniform and variable-density random sampling, as well as equidistantly spaced scan-lines, improving mean absolute reconstruction error by 15%. Moreover, posterior inference and the sampling scheme generation are performed in just 0.015 seconds (66Hz), making it fast enough for real-time 2D ultrasound imaging applications.

M. M. A. Valiuddin, R. J. G. van Sloun, C. G. A. Viviers et al.

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for robust decision-making. The resulting reliance on point estimates has fueled interest in probabilistic segmentation, but the literature remains fragmented. In response, this review consolidates and contextualizes foundational concepts in uncertainty modeling, including the non-trivial task of distinguishing between epistemic and aleatoric uncertainty and examining their roles across four key downstream segmentation tasks, highlighting Active Learning as particularly promising. By unifying theory, terminology, and applications, we provide a coherent foundation for researchers and identify critical challenges, such as strong assumptions in spatial aggregation, lack of standardized benchmarks, and pitfalls in current uncertainty quantification methods. We identify trends such as the adoption of contemporary generative models, driven by advances in the broader field of generative modeling, with segmentation-specific innovation primarily in the conditioning mechanisms. Moreover, we observe growing interest in distribution- and sampling-free approaches to uncertainty estimation. We further propose directions for advancing uncertainty-aware segmentation in deep learning, including pragmatic strategies for disentangling different sources of uncertainty, novel uncertainty modeling approaches and improved Transformer-based backbones. In this way, we aim to support the development of more reliable, efficient, and interpretable segmentation models that effectively incorporate uncertainty into real-world applications.

Ivana Nikoloska, Ruud Van Sloun, Osvaldo Simeone

Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of classical sensors. However, identifying suitable sensing probes and measurement schemes can be a classically intractable task, as it requires optimizing over Hilbert spaces of high dimension. In variational quantum sensing, a probe quantum system is generated via a parameterized quantum circuit (PQC), exposed to an unknown physical parameter through a quantum channel, and measured to collect classical data. PQCs and measurements are typically optimized using offline strategies based on frequentist learning criteria. This paper introduces an adaptive protocol that uses Bayesian inference to optimize the sensing policy via the maximization of the active information gain. The proposed variational methodology is tailored for non-asymptotic regimes where a single probe can be deployed in each time step, and is extended to support the fusion of estimates from multiple quantum sensing agents.

Julian P. Merkofer, Dennis M. J. van de Sande, Alex A. Bhogal et al.

Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cramér-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.

Han Wang, Eduardo Pérez, Iris A. M. Huijben et al.

Multidimensional data acquisition often requires extensive time and poses significant challenges for hardware and software regarding data storage and processing. Rather than designing a single compression matrix as in conventional compressed sensing, structured compressed sensing yields dimension-specific compression matrices, reducing the number of optimizable parameters. Recent advances in machine learning (ML) have enabled task-based supervised learning of subsampling matrices, albeit at the expense of complex downstream models. Additionally, the sampling resource allocation across dimensions is often determined in advance through heuristics. To address these challenges, we introduce Structured COmpressed Sensing with Automatic Resource Allocation (SCOSARA) with an information theory-based unsupervised learning strategy. SCOSARA adaptively distributes samples across sampling dimensions while maximizing Fisher information content. Using ultrasound localization as a case study, we compare SCOSARA to state-of-the-art ML-based and greedy search algorithms. Simulation results demonstrate that SCOSARA can produce high-quality subsampling matrices that achieve lower Cramér-Rao Bound values than the baselines. In addition, SCOSARA outperforms other ML-based algorithms in terms of the number of trainable parameters, computational complexity, and memory requirements while automatically choosing the number of samples per axis.

Roelof G. Hup, Julian P. Merkofer, Alex A. Bhogal et al.

Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability challenges with large datasets due to computational demands, and experience reduced performance with high-dimensional or intricate data, as well as hidden anomalies. Furthermore, they often lack interpretability and adaptability to domain-specific knowledge, which limits their versatility across different fields. In this work, we propose a deep learning-based CPD/AD method called Probabilistic Predictive Coding (PPC) that jointly learns to encode sequential data to low dimensional latent space representations and to predict the subsequent data representations as well as the corresponding prediction uncertainties. The model parameters are optimized with maximum likelihood estimation by comparing these predictions with the true encodings. At the time of application, the true and predicted encodings are used to determine the probability of conformity, an interpretable and meaningful anomaly score. Furthermore, our approach has linear time complexity, scalability issues are prevented, and the method can easily be adjusted to a wide range of data types and intricate applications. We demonstrate the effectiveness and adaptability of our proposed method across synthetic time series experiments, image data, and real-world magnetic resonance spectroscopic imaging data.

Iris A. M. Huijben, Matthijs Douze, Matthew Muckley et al.

Vector quantization is a fundamental operation for data compression and vector search. To obtain high accuracy, multi-codebook methods represent each vector using codewords across several codebooks. Residual quantization (RQ) is one such method, which iteratively quantizes the error of the previous step. While the error distribution is dependent on previously-selected codewords, this dependency is not accounted for in conventional RQ as it uses a fixed codebook per quantization step. In this paper, we propose QINCo, a neural RQ variant that constructs specialized codebooks per step that depend on the approximation of the vector from previous steps. Experiments show that QINCo outperforms state-of-the-art methods by a large margin on several datasets and code sizes. For example, QINCo achieves better nearest-neighbor search accuracy using 12-byte codes than the state-of-the-art UNQ using 16 bytes on the BigANN1M and Deep1M datasets.

Tristan S. W. Stevens, Nishith Chennakeshava, Frederik J. de Bruijn et al.

Intravascular ultrasound (IVUS) offers a unique perspective in the treatment of vascular diseases by creating a sequence of ultrasound-slices acquired from within the vessel. However, unlike conventional hand-held ultrasound, the thin catheter only provides room for a small number of physical channels for signal transfer from a transducer-array at the tip. For continued improvement of image quality and frame rate, we present the use of deep reinforcement learning to deal with the current physical information bottleneck. Valuable inspiration has come from the field of magnetic resonance imaging (MRI), where learned acquisition schemes have brought significant acceleration in image acquisition at competing image quality. To efficiently accelerate IVUS imaging, we propose a framework that utilizes deep reinforcement learning for an optimal adaptive acquisition policy on a per-frame basis enabled by actor-critic methods and Gumbel top-$K$ sampling.

Vincent van de Schaft, Ruud J. G. van Sloun

Ultrasonography offers an inexpensive, widely-accessible and compact medical imaging solution. However, compared to other imaging modalities such as CT and MRI, ultrasound images notoriously suffer from strong speckle noise, which originates from the random interference of sub-wavelength scattering. This deteriorates ultrasound image quality and makes interpretation challenging. We here propose a new unsupervised ultrasound speckle reduction and image denoising method based on maximum-a-posteriori estimation with deep generative priors that are learned from high-quality MRI images. To model the generative tissue reflectivity prior, we exploit normalizing flows, which in recent years have shown to be very powerful in modeling signal priors across a variety of applications. To facilitate generaliation, we factorize the prior and train our flow model on patches from the NYU fastMRI (fully-sampled) dataset. This prior is then used for inference in an iterative denoising scheme. We first validate the utility of our learned priors on noisy MRI data (no prior domain shift), and then turn to evaluating performance on both simulated and in-vivo ultrasound images from the PICMUS and CUBDL datasets. The results show that the method outperforms other (unsupervised) ultrasound denoising methods (NLM and OBNLM) both quantitatively and qualitatively.

Guy Revach, Nir Shlezinger, Timur Locher et al.

In this paper we adapt KalmanNet, which is a recently pro-posed deep neural network (DNN)-aided system whose architecture follows the operation of the model-based Kalman filter (KF), to learn its mapping in an unsupervised manner, i.e., without requiring ground-truth states. The unsupervised adaptation is achieved by exploiting the hybrid model-based/data-driven architecture of KalmanNet, which internally predicts the next observation as the KF does. These internal features are then used to compute the loss rather than the state estimate at the output of the system. With the capability of unsupervised learning, one can use KalmanNet not only to track the hidden state, but also to adapt to variations in the state space (SS) model. We numerically demonstrate that when the noise statistics are unknown, unsupervised KalmanNet achieves a similar performance to KalmanNet with supervised learning. We also show that we can adapt a pre-trained KalmanNet to changing SS models without providing additional data thanks to the unsupervised capabilities.

Itzik Klein, Guy Revach, Nir Shlezinger et al.

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the underlying statistics, however, deep learning based tracking systems struggle to reliably characterize uncertainty. In this paper, we investigate the ability of KalmanNet, a recently proposed hybrid model-based deep state tracking algorithm, to estimate an uncertainty measure. By exploiting the interpretable nature of KalmanNet, we show that the error covariance matrix can be computed based on its internal features, as an uncertainty measure. We demonstrate that when the system dynamics are known, KalmanNet-which learns its mapping from data without access to the statistics-provides uncertainty similar to that provided by the KF; and while in the presence of evolution model-mismatch, KalmanNet pro-vides a more accurate error estimation.

Iris A. M. Huijben, Wouter Kool, Max B. Paulus et al.

The Gumbel-max trick is a method to draw a sample from a categorical distribution, given by its unnormalized (log-)probabilities. Over the past years, the machine learning community has proposed several extensions of this trick to facilitate, e.g., drawing multiple samples, sampling from structured domains, or gradient estimation for error backpropagation in neural network optimization. The goal of this survey article is to present background about the Gumbel-max trick, and to provide a structured overview of its extensions to ease algorithm selection. Moreover, it presents a comprehensive outline of (machine learning) literature in which Gumbel-based algorithms have been leveraged, reviews commonly-made design choices, and sketches a future perspective.

Ruud JG van Sloun, Jong Chul Ye, Yonina C Eldar

Diagnostic imaging plays a critical role in healthcare, serving as a fundamental asset for timely diagnosis, disease staging and management as well as for treatment choice, planning, guidance, and follow-up. Among the diagnostic imaging options, ultrasound imaging is uniquely positioned, being a highly cost-effective modality that offers the clinician an unmatched and invaluable level of interaction, enabled by its real-time nature. Ultrasound probes are becoming increasingly compact and portable, with the market demand for low-cost pocket-sized and (in-body) miniaturized devices expanding. At the same time, there is a strong trend towards 3D imaging and the use of high-frame-rate imaging schemes; both accompanied by dramatically increasing data rates that pose a heavy burden on the probe-system communication and subsequent image reconstruction algorithms. With the demand for high-quality image reconstruction and signal extraction from less (e.g unfocused or parallel) transmissions that facilitate fast imaging, and a push towards compact probes, modern ultrasound imaging leans heavily on innovations in powerful digital receive channel processing. Beamforming, the process of mapping received ultrasound echoes to the spatial image domain, naturally lies at the heart of the ultrasound image formation chain. In this chapter on Deep Learning for Ultrasound Beamforming, we discuss why and when deep learning methods can play a compelling role in the digital beamforming pipeline, and then show how these data-driven systems can be leveraged for improved ultrasound image reconstruction.

Julian P. Merkofer, Guy Revach, Nir Shlezinger et al.

Direction of arrival (DoA) estimation of multiple signals is pivotal in sensor array signal processing. A popular multi-signal DoA estimation method is the multiple signal classification (MUSIC) algorithm, which enables high-performance super-resolution DoA recovery while being highly applicable in practice. MUSIC is a model-based algorithm, relying on an accurate mathematical description of the relationship between the signals and the measurements and assumptions on the signals themselves (non-coherent, narrowband sources). As such, it is sensitive to model imperfections. In this work we propose to overcome these limitations of MUSIC by augmenting the algorithm with specifically designed neural architectures. Our proposed deep augmented MUSIC (DA-MUSIC) algorithm is thus a hybrid model-based/data-driven DoA estimator, which leverages data to improve performance and robustness while preserving the interpretable flow of the classic method. DA-MUSIC is shown to learn to overcome limitations of the purely model-based method, such as its inability to successfully localize coherent sources as well as estimate the number of coherent signal sources present. We further demonstrate the superior resolution of the DA-MUSIC algorithm in synthetic narrowband and broadband scenarios as well as with real-world data of DoA estimation from seismic signals.

M. M. A. Valiuddin, C. G. A. Viviers, R. J. G. van Sloun et al.

Quantifying uncertainty in medical image segmentation applications is essential, as it is often connected to vital decision-making. Compelling attempts have been made in quantifying the uncertainty in image segmentation architectures, e.g. to learn a density segmentation model conditioned on the input image. Typical work in this field restricts these learnt densities to be strictly Gaussian. In this paper, we propose to use a more flexible approach by introducing Normalizing Flows (NFs), which enables the learnt densities to be more complex and facilitate more accurate modeling for uncertainty. We prove this hypothesis by adopting the Probabilistic U-Net and augmenting the posterior density with an NF, allowing it to be more expressive. Our qualitative as well as quantitative (GED and IoU) evaluations on the multi-annotated and single-annotated LIDC-IDRI and Kvasir-SEG segmentation datasets, respectively, show a clear improvement. This is mostly apparent in the quantification of aleatoric uncertainty and the increased predictive performance of up to 14 percent. This result strongly indicates that a more flexible density model should be seriously considered in architectures that attempt to capture segmentation ambiguity through density modeling. The benefit of this improved modeling will increase human confidence in annotation and segmentation, and enable eager adoption of the technology in practice.

Guy Revach, Nir Shlezinger, Xiaoyong Ni et al.

State estimation of dynamical systems in real-time is a fundamental task in signal processing. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low complexity optimal solution. However, both linearity of the underlying SS model and accurate knowledge of it are often not encountered in practice. Here, we present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics with partial information. By incorporating the structural SS model with a dedicated recurrent neural network module in the flow of the KF, we retain data efficiency and interpretability of the classic algorithm while implicitly learning complex dynamics from data. We demonstrate numerically that KalmanNet overcomes non-linearities and model mismatch, outperforming classic filtering methods operating with both mismatched and accurate domain knowledge.

Lizeth Gonzalez-Carabarin, Iris A. M. Huijben, Bastiaan S. Veeling et al.

Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and complex control logic that diminishes the benefits of unstructured pruning. This has spurred structured coarse-grained pruning solutions that prune entire filters or even layers, enabling efficient implementation at the expense of reduced flexibility. Here we propose a flexible new pruning mechanism that facilitates pruning at different granularities (weights, kernels, filters/feature maps), while retaining efficient memory organization (e.g. pruning exactly k-out-of-n weights for every output neuron, or pruning exactly k-out-of-n kernels for every feature map). We refer to this algorithm as Dynamic Probabilistic Pruning (DPP). DPP leverages the Gumbel-softmax relaxation for differentiable k-out-of-n sampling, facilitating end-to-end optimization. We show that DPP achieves competitive compression rates and classification accuracy when pruning common deep learning models trained on different benchmark datasets for image classification. Relevantly, the non-magnitude-based nature of DPP allows for joint optimization of pruning and weight quantization in order to even further compress the network, which we show as well. Finally, we propose novel information theoretic metrics that show the confidence and pruning diversity of pruning masks within a layer.

Iris A. M. Huijben, Bastiaan S. Veeling, Ruud J. G. van Sloun

Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received significant attention, with many CS MRI methods exploiting variable-density probability distributions. Realizing that an optimal sampling pattern may depend on the downstream task (e.g. image reconstruction, segmentation, or classification), we here propose joint learning of both task-adaptive k-space sampling and a subsequent model-based proximal-gradient recovery network. The former is enabled through a probabilistic generative model that leverages the Gumbel-softmax relaxation to sample across trainable beliefs while maintaining differentiability. The proposed combination of a highly flexible sampling model and a model-based (sampling-adaptive) image reconstruction network facilitates exploration and efficient training, yielding improved MR image quality compared to other sampling baselines.

R. R. Wildeboer, R. J. G. van Sloun, C. K. Mannaerts et al.

Shear-wave elastography (SWE) permits local estimation of tissue elasticity, an important imaging marker in biomedicine. This recently-developed, advanced technique assesses the speed of a laterally-travelling shear wave after an acoustic radiation force "push" to estimate local Young's moduli in an operator-independent fashion. In this work, we show how synthetic SWE (sSWE) images can be generated based on conventional B-mode imaging through deep learning. Using side-by-side-view B-mode/SWE images collected in 50 patients with prostate cancer, we show that sSWE images with a pixel-wise mean absolute error of 4.5+/-0.96 kPa with regard to the original SWE can be generated. Visualization of high-level feature levels through t-Distributed Stochastic Neighbor Embedding reveals substantial overlap between data from two different scanners. Qualitatively, we examined the use of the sSWE methodology for B-mode images obtained with a scanner without SWE functionality. We also examined the use of this type of network in elasticity imaging in the thyroid. Limitations of the technique reside in the fact that networks have to be retrained for different organs, and that the method requires standardization of the imaging settings and procedure. Future research will be aimed at development of sSWE as an elasticity-related tissue typing strategy that is solely based on B-mode ultrasound acquisition, and the examination of its clinical utility.

Ruud JG van Sloun, Regev Cohen, Yonina C Eldar

We consider deep learning strategies in ultrasound systems, from the front-end to advanced applications. Our goal is to provide the reader with a broad understanding of the possible impact of deep learning methodologies on many aspects of ultrasound imaging. In particular, we discuss methods that lie at the interface of signal acquisition and machine learning, exploiting both data structure (e.g. sparsity in some domain) and data dimensionality (big data) already at the raw radio-frequency channel stage. As some examples, we outline efficient and effective deep learning solutions for adaptive beamforming and adaptive spectral Doppler through artificial agents, learn compressive encodings for color Doppler, and provide a framework for structured signal recovery by learning fast approximations of iterative minimization problems, with applications to clutter suppression and super-resolution ultrasound. These emerging technologies may have considerable impact on ultrasound imaging, showing promise across key components in the receive processing chain.

Oren Solomon, Regev Cohen, Yi Zhang et al.

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of a low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and the fast iterative shrinkage algorithm, and show that our architecture exhibits better image quality and contrast.

Ruud J. G. van Sloun, Oren Solomon, Matthew Bruce et al.

Ultrasound localization microscopy has enabled super-resolution vascular imaging through precise localization of individual ultrasound contrast agents (microbubbles) across numerous imaging frames. However, analysis of high-density regions with significant overlaps among the microbubble point spread responses yields high localization errors, constraining the technique to low-concentration conditions. As such, long acquisition times are required to sufficiently cover the vascular bed. In this work, we present a fast and precise method for obtaining super-resolution vascular images from high-density contrast-enhanced ultrasound imaging data. This method, which we term Deep Ultrasound Localization Microscopy (Deep-ULM), exploits modern deep learning strategies and employs a convolutional neural network to perform localization microscopy in dense scenarios. This end-to-end fully convolutional neural network architecture is trained effectively using on-line synthesized data, enabling robust inference in-vivo under a wide variety of imaging conditions. We show that deep learning attains super-resolution with challenging contrast-agent densities, both in-silico as well as in-vivo. Deep-ULM is suitable for real-time applications, resolving about 70 high-resolution patches (128x128 pixels) per second on a standard PC. Exploiting GPU computation, this number increases to 1250 patches per second.