Data-driven Priors Research Articles

Event-horizon-scale Imaging of M87* under Different Assumptions via Deep Generative Image Priors

Reconstructing images from the Event Horizon Telescope (EHT) observations of M87*, the supermassive black hole at the center of the galaxy M87, depends on a prior to impose desired image statistics. However, given the impossibility of directly observing black holes, there is no clear choice for a prior. We present a framework for flexibly designing a range of priors, each bringing different biases to the image reconstruction. These priors can be weak (e.g., impose only basic natural-image statistics) or strong (e.g., impose assumptions of black hole structure). Our framework uses Bayesian inference with score-based priors, which are data-driven priors arising from a deep generative model that can learn complicated image distributions. Using our Bayesian imaging approach with sophisticated data-driven priors, we can assess how visual features and uncertainty of reconstructed images change depending on the prior. In addition to simulated data, we image the real EHT M87* data and discuss how recovered features are influenced by the choice of prior.

Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging

Abstract Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in handling the deluge and complexity of incoming data. This challenge requires building radio interferometric (RI) imaging methods that can cope with the massive data sizes and provide high-quality image reconstructions with uncertainty quantification (UQ). This work proposes a method coined QuantifAI to address UQ in RI imaging with data-driven (learned) priors for high-dimensional settings. Our model, rooted in the Bayesian framework, uses a physically motivated model for the likelihood. The model exploits a data-driven convex prior potential, which can encode complex information learned implicitly from simulations and guarantee the log-concavity of the posterior. We leverage probability concentration phenomena of high-dimensional log-concave posteriors to obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimisation methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC strategies. QuantifAI allows us to compute local credible intervals and perform hypothesis testing of structure on the reconstructed image. We propose a novel fast method to compute pixel-wise uncertainties at different scales, which uses 3 and 6 orders of magnitude less likelihood evaluations than other UQ methods like length of the credible intervals and Monte Carlo posterior sampling, respectively. We demonstrate our method by reconstructing RI images in a simulated setting and carrying out fast and scalable UQ, which we validate with MCMC sampling. Our method shows an improved image quality and more meaningful uncertainties than the benchmark method based on a sparsity-promoting prior. QuantifAI’s source code is available from https://github.com/astro-informatics/QuantifAI.

Optimal constraints on Primordial non-Gaussianity with the eBOSS DR16 quasars in Fourier space

We present constraints on the amplitude of local Primordial Non-Gaussianities (PNG), f NL, using the quasar sample in the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16). We analyze the power spectrum monopole, testing for the presence of scale-dependent galaxy bias induced by local PNG. Our analysis makes use of optimal redshift weights that maximize the response of the quasar sample to the possible presence of non-zero PNG. We find -4 < f NL < 27 at 68% confidence level, which is among the strongest bounds with Large Scale Structure data. The optimal analysis reduces the error bar by ~10% compared to the standard one, but this improvement is lower than the one expected from previous forecasts. In addition, the larger volume of this dataset, when compared to previous releases of the eBOSS quasar catalog, does not always correspond to a reduction of the final uncertainty on local PNG. This could suggest the presence of still unknown systematic effects in the data.If the quasars have a lower response to local PNG, our optimal constraint becomes -23 < f NL < 21 at 68%, with an improvement of 30% over standardanalyses. We alsoshow how to use the optimal weights to put data-driven priors on the sample's response tolocal PNG.

Learning data distribution of three-dimensional ocean sound speed fields via diffusion models.

The probability distribution of three-dimensional sound speed fields (3D SSFs) in an ocean region encapsulates vital information about their variations, serving as valuable data-driven priors for SSF inversion tasks. However, learning such a distribution is challenging due to the high dimensionality and complexity of 3D SSFs. To tackle this challenge, we propose employing the diffusion model, a cutting-edge deep generative model that has showcased remarkable performance in diverse domains, including image and audio processing. Nonetheless, applying this approach to 3D ocean SSFs encounters two primary hurdles. First, the lack of publicly available well-crafted 3D SSF datasets impedes training and evaluation. Second, 3D SSF data consist of multiple 2D layers with varying variances, which can lead to uneven denoising during the reverse process. To surmount these obstacles, we introduce a novel 3D SSF dataset called 3DSSF, specifically designed for training and evaluating deep generative models. In addition, we devise a high-capacity neural architecture for the diffusion model to effectively handle variations in 3D sound speeds. Furthermore, we employ state-of-the-art continuous-time-based optimization method and predictor-corrector scheme for high-performance training and sampling. Notably, this paper presents the first evaluation of the diffusion model's effectiveness in generating 3D SSF data. Numerical experiments validate the proposed method's strong ability to learn the underlying data distribution of 3D SSFs, and highlight its effectiveness in assisting SSF inversion tasks and subsequently characterizing the transmission loss of underwater acoustics.

Image Reconstruction for Accelerated MR Scan With Faster Fourier Convolutional Neural Networks.

High quality image reconstruction from undersampled k -space data is key to accelerating MR scanning. Current deep learning methods are limited by the small receptive fields in reconstruction networks, which restrict the exploitation of long-range information, and impede the mitigation of full-image artifacts, particularly in 3D reconstruction tasks. Additionally, the substantial computational demands of 3D reconstruction considerably hinder advancements in related fields. To tackle these challenges, we propose the following: 1) A novel convolution operator named Faster Fourier Convolution (FasterFC), aims at providing an adaptable broad receptive field for spatial domain reconstruction networks with fast computational speed. 2) A split-slice strategy that substantially reduces the computational load of 3D reconstruction, enabling high-resolution, multi-coil, 3D MR image reconstruction while fully utilizing inter-layer and intra-layer information. 3) A single-to-group algorithm that efficiently utilizes scan-specific and data-driven priors to enhance k -space interpolation effects. 4) A multi-stage, multi-coil, 3D fast MRI method, called the faster Fourier convolution based single-to-group network (FAS-Net), comprising a single-to-group k -space interpolation algorithm and a FasterFC-based image domain reconstruction module, significantly minimizes the computational demands of 3D reconstruction through split-slice strategy. Experimental evaluations conducted on the NYU fastMRI and Stanford MRI Data datasets reveal that the FasterFC significantly enhances the quality of both 2D and 3D reconstruction results. Moreover, FAS-Net, characterized as a method that can achieve high-resolution (320, 320, 256), multi-coil, (8 coils), 3D fast MRI, exhibits superior reconstruction performance compared to other state-of-the-art 2D and 3D methods.

Parallel-stream fusion of scan-specific and scan-general priors for learning deep MRI reconstruction in low-data regimes

Magnetic resonance imaging (MRI) is an essential diagnostic tool that suffers from prolonged scan times. Reconstruction methods can alleviate this limitation by recovering clinically usable images from accelerated acquisitions. In particular, learning-based methods promise performance leaps by employing deep neural networks as data-driven priors. A powerful approach uses scan-specific (SS) priors that leverage information regarding the underlying physical signal model for reconstruction. SS priors are learned on each individual test scan without the need for a training dataset, albeit they suffer from computationally burdening inference with nonlinear networks. An alternative approach uses scan-general (SG) priors that instead leverage information regarding the latent features of MRI images for reconstruction. SG priors are frozen at test time for efficiency, albeit they require learning from a large training dataset. Here, we introduce a novel parallel-stream fusion model (PSFNet) that synergistically fuses SS and SG priors for performant MRI reconstruction in low-data regimes, while maintaining competitive inference times to SG methods. PSFNet implements its SG prior based on a nonlinear network, yet it forms its SS prior based on a linear network to maintain efficiency. A pervasive framework for combining multiple priors in MRI reconstruction is algorithmic unrolling that uses serially alternated projections, causing error propagation under low-data regimes. To alleviate error propagation, PSFNet combines its SS and SG priors via a novel parallel-stream architecture with learnable fusion parameters. Demonstrations are performed on multi-coil brain MRI for varying amounts of training data. PSFNet outperforms SG methods in low-data regimes, and surpasses SS methods with few tens of training samples. On average across tasks, PSFNet achieves 3.1 dB higher PSNR, 2.8% higher SSIM, and 0.3 × lower RMSE than baselines. Furthermore, in both supervised and unsupervised setups, PSFNet requires an order of magnitude lower samples compared to SG methods, and enables an order of magnitude faster inference compared to SS methods. Thus, the proposed model improves deep MRI reconstruction with elevated learning and computational efficiency.

Flexible and High-Gain DOFS Deconvolution Based on Data-Driven Denoising Prior

Spatial resolution is an essential parameter for distributed optical fiber sensing (DOFS). Deconvolution is a promising solution to improve spatial resolution because of its good universality and ability to restore infinitely high spatial resolution in theory. However, conventional iterative deconvolution algorithms require manually designed priors, which makes it difficult to restore the signal accurately. Although end-to-end methods based on artificial neural networks provide more accurate results based on data-driven priors, a neural network can only be applied to data with similar characteristics to its training data. For systems with different parameters, the neural network needs to be retrained or fine-tuned, which is time and computational resource consuming. Here, we employ a new deconvolution method for DOFS based on half-quadratic splitting and denoising neural networks that exploits the advantages of both iterative and machine learning methods. Besides, we propose a method to calculate the deconvolution gain to evaluate the deconvolution performance quantitatively. In an experiment with 10 deconvolution ratios, the deconvolution gain of the employed method is 15.8 dB, while that of a conventional iterative method and an end-to-end machine learning method are 7.9 dB and 15 dB, respectively. Moreover, this new deconvolution method can be adapted to data with arbitrary system parameters, making it more flexible than end-to-end neural networks in practical applications.

Hyperparameter importance and optimization of quantum neural networks across small datasets

As restricted quantum computers become available, research focuses on finding meaningful applications. For example, in quantum machine learning, a special type of quantum circuit called a quantum neural network is one of the most investigated approaches. However, we know little about suitable circuit architectures or important model hyperparameters for a given task. In this work, we apply the functional ANOVA framework to the quantum neural network architectures to analyze which of the quantum machine learning hyperparameters are most influential for their predictive performance. We restrict our study to 7 open-source datasets from the OpenML-CC18 classification benchmark, which are small enough for simulations on quantum hardware with fewer than 20 qubits. Using this framework, three main levels of importance were identified, confirming expected patterns and revealing new insights. For instance, the learning rate is identified as the most important hyperparameter on all datasets, whereas the particular choice of entangling gates used is found to be the least important on all except for one dataset. In addition to identifying the relevant hyperparameters, for each of them, we also learned data-driven priors based on values that perform well on previously seen datasets, which can then be used to steer hyperparameter optimization processes. We utilize these priors in the hyperparameter optimization method hyperband and show that these improve performance against uniform sampling across all datasets by, on average, 0.53%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.53 \\%$$\\end{document}, up to 6.11%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6.11 \\%$$\\end{document}, in cross-validation accuracy. We also demonstrate that such improvements hold on average regardless of the configuration hyperband is run with. Our work introduces new methodologies for studying quantum machine learning models toward quantum model selection in practice. All research code is made publicly available.

VAEs with structured image covariance applied to compressed sensing MRI

Objective.This paper investigates how generative models, trained on ground-truth images, can be used as priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned regularization will provide complex data-driven priors to inverse problems while still retaining the control and insight of a variational regularization method. Moreover, unsupervised learning, without paired training data, allows the learned regularizer to remain flexible to changes in the forward problem such as noise level, sampling pattern or coil sensitivities in MRI. Approach. We utilize variational autoencoders that generate not only an image but also a covariance uncertainty matrix for each image. The covariance can model changing uncertainty dependencies caused by structure in the image, such as edges or objects, and provides a new distance metric from the manifold of learned images. Main results. We evaluate these novel generative regularizers on retrospectively sub-sampled real-valued MRI measurements from the fastMRI dataset. We compare our proposed learned regularization against other unlearned regularization approaches and unsupervised and supervised deep learning methods. Significance. Our results show that the proposed method is competitive with other state-of-the-art methods and behaves consistently with changing sampling patterns and noise levels.

Machine learning based priors for Bayesian inversion in MR imaging

The Bayesian approach allows the incorporation of informative prior knowledge to effectively enable and improve the solution of inverse problems. Obtaining prior information in probabilistic terms is, however, a challenging task. Recently, machine learning has been applied for the training of generative models to facilitate the translation of historically or otherwise available data to a prior distribution. In this work, we apply this methodology to undersampled magnetic resonance imaging. In particular, we employ an autoencoder as part of a generative model to statistically regularise and solve the high-dimensional inverse problem using Bayesian inversion. Comparison with a classical Gaussian Markov random field prior is performed and numerical examples highlight the possible advantages of data-driven priors.

DeepSTI: Towards tensor reconstruction using fewer orientations in susceptibility tensor imaging.

Susceptibility tensor imaging (STI) is an emerging magnetic resonance imaging technique that characterizes the anisotropic tissue magnetic susceptibility with a second-order tensor model. STI has the potential to provide information for both the reconstruction of white matter fiber pathways and detection of myelin changes in the brain at mm resolution or less, which would be of great value for understanding brain structure and function in healthy and diseased brain. However, the application of STI in vivo has been hindered by its cumbersome and time-consuming acquisition requirement of measuring susceptibility induced MR phase changes at multiple head orientations. Usually, sampling at more than six orientations is required to obtain sufficient information for the ill-posed STI dipole inversion. This complexity is enhanced by the limitation in head rotation angles due to physical constraints of the head coil. As a result, STI has not yet been widely applied in human studies in vivo. In this work, we tackle these issues by proposing an image reconstruction algorithm for STI that leverages data-driven priors. Our method, called DeepSTI, learns the data prior implicitly via a deep neural network that approximates the proximal operator of a regularizer function for STI. The dipole inversion problem is then solved iteratively using the learned proximal network. Experimental results using both simulation and in vivo human data demonstrate great improvement over state-of-the-art algorithms in terms of the reconstructed tensor image, principal eigenvector maps and tractography results, while allowing for tensor reconstruction with MR phase measured at much less than six different orientations. Notably, promising reconstruction results are achieved by our method from only one orientation in human in vivo, and we demonstrate a potential application of this technique for estimating lesion susceptibility anisotropy in patients with multiple sclerosis.

Association of Non-Invasive Respiratory Support with Extubation Outcomes in Brain-Injured Patients Receiving Mechanical Ventilation: A Secondary Analysis of ENIO.

Non-invasive respiratory support using high flow nasal cannula (HFNC) or non-invasive positive pressure ventilation (NIPPV) can decrease the risk of reintubation in patients being liberated from mechanical ventilation, but effects in patients with acute brain injury are unknown. To evaluate the association between post-extubation non-invasive respiratory support and reintubation in patients with acute brain injury being liberated from mechanical ventilation. This was a secondary analysis of a prospective, observational study of mechanically ventilated patients with acute brain injury (NCT03400904). The primary endpoint was reintubation during ICU admission. We used mixed effects logistic regression models with patient-level covariates and random intercepts for hospital and country to evaluate the association between prophylactic (i.e, planned) HFNC or NIPPV and reintubation. 1,115 patients were included from 62 hospitals and 19 countries, of whom 267 received HFNC or NIPPV following extubation (23.9%). Compared to conventional oxygen therapy, neither prophylactic HFNC nor NIPPV was associated with decreased risk of reintubation (respectively, odds ratio (OR), 0.97; 95% confidence interval (CI), 0.54-1.73; OR, 0.63; 95%CI, 0.30-1.32). Findings remained consistent in sensitivity analyses accounting for alternate adjustment procedures, missing data, shorter timeframes of extubation failure, and competing risks precluding reintubation. In a Bayesian analysis using skeptical and data-driven priors, the probability of reduced reintubation ranged from 17-34% for HFNC and 46-74% for NIPPV. In a large cohort of brain-injured patients undergoing liberation from mechanical ventilation, prophylactic use of HFNC and NIPPV were not associated with reintubation. Prospective trials are needed to explore treatment effects in this population.

Deep unfolding multi-scale regularizer network for image denoising

Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps, and utilize convolutional neural networks (CNNs) to learn data-driven priors. However, their performance is limited for two main reasons. Firstly, priors learned in deep feature space need to be converted to the image space at each iteration step, which limits the depth of CNNs and prevents CNNs from exploiting contextual information. Secondly, existing methods only learn deep priors at the single full-resolution scale, so ignore the benefits of multi-scale context in dealing with high level noise. To address these issues, we explicitly consider the image denoising process in the deep feature space and propose the deep unfolding multi-scale regularizer network (DUMRN) for image denoising. The core of DUMRN is the feature-based denoising module (FDM) that directly removes noise in the deep feature space. In each FDM, we construct a multi-scale regularizer block to learn deep prior information from multi-resolution features. We build the DUMRN by stacking a sequence of FDMs and train it in an end-to-end manner. Experimental results on synthetic and real-world benchmarks demonstrate that DUMRN performs favorably compared to state-of-the-art methods.

Hyperspectral Image Superresolution via Subspace-Based Deep Prior Regularization

Hyperspectral imaging is able to provide a finer delivery of various material properties than conventional imaging systems. Yet in reality, an optical system can only generate data with high spatial resolution but low spectral one, or vice versa, at video rates. As a result, an issue that fuses low-resolution hyperspectral (LRHS) and high-resolution multispectral (HRMS) images has gained great attention. However, most fusion approaches depend purely on hand-crafted regularizers or data-driven priors, leading to the issues of tricky parameter selection or poor interpretability. In this work, a subspace-based deep prior regularization (SDPR) is proposed to tackle these problems, which takes both hand-crafted regularizer and data-driven prior into account. Specifically, we leverage the spectral correlation of the images and transfer them from the original space to the subspace domain, within which a modified U-net-based deep prior learning network (SDPL-net) is designed for the fusion issue. Moreover, instead of taking the output of SDPL-net directly as the result, we further feed the output back to the model-based optimization. Under such prior regularization, the recovered high-resolution hyperspectral (HRHS) image holds a high consistency to its inherent structure and hence tends to present enhanced reliability and accuracy. Experimental results on simulated and real data reveal that the proposed method excels other state-of-the-art (SOTA) methods in both quantitative and qualitative metrics.

Shape From Polarization With Distant Lighting Estimation.

This article presents a new approach for surface normal recovery from polarization images under an unknown distant light. Polarization provides rich cues of object geometry and material, but it is also influenced by different lighting conditions. Different from previous Shape-from-Polarization (SfP) methods, which rely on handcrafted or data-driven priors, we analytically investigate the benefits of estimating distant lighting for resolving the ambiguity in normal estimation from SfP using the polarimetric Bidirectional Reflectance Distribution Function (pBRDF) based image formation model. We then propose a two-stage learning framework that first effectively exploits polarization and shading cues to estimate the reflectance and lighting information and then optimizes the initial normal as the geometric prior. Leveraging the normal prior with the polarization cues from the input images, our network further generates the surface normal with more details in the second stage. We also present a data generation pipeline derived from the pBRDF model enabling model training and create a real dataset for evaluation of SfP approaches. Extensive ablation studies show the effectiveness of our designed architecture, and our approach outperforms existing methods in quantitative and qualitative experiments on real data.

Deep Spatial-Angular Regularization for Light Field Imaging, Denoising, and Super-Resolution.

Coded aperture is a promising approach for capturing the 4-D light field (LF), in which the 4-D data are compressively modulated into 2-D coded measurements that are further decoded by reconstruction algorithms. The bottleneck lies in the reconstruction algorithms, resulting in rather limited reconstruction quality. To tackle this challenge, we propose a novel learning-based framework for the reconstruction of high-quality LFs from acquisitions via learned coded apertures. The proposed method incorporates the measurement observation into the deep learning framework elegantly to avoid relying entirely on data-driven priors for LF reconstruction. Specifically, we first formulate the compressive LF reconstruction as an inverse problem with an implicit regularization term. Then, we construct the regularization term with a deep efficient spatial-angular separable convolutional sub-network in the form of local and global residual learning to comprehensively explore the signal distribution free from the limited representation ability and inefficiency of deterministic mathematical modeling. Furthermore, we extend this pipeline to LF denoising and spatial super-resolution, which could be considered as variants of coded aperture imaging equipped with different degradation matrices. Extensive experimental results demonstrate that the proposed methods outperform state-of-the-art approaches to a significant extent both quantitatively and qualitatively, i.e., the reconstructed LFs not only achieve much higher PSNR/SSIM but also preserve the LF parallax structure better on both real and synthetic LF benchmarks. The code will be publicly available at https://github.com/MantangGuo/DRLF.

Neural Interferometry: Image Reconstruction from Astronomical Interferometers Using Transformer-Conditioned Neural Fields

Astronomical interferometry enables a collection of telescopes to achieve angular resolutions comparable to that of a single, much larger telescope. This is achieved by combining simultaneous observations from pairs of telescopes such that the signal is mathematically equivalent to sampling the Fourier domain of the object. However, reconstructing images from such sparse sampling is a challenging and ill-posed problem, with current methods requiring precise tuning of parameters and manual, iterative cleaning by experts. We present a novel deep learning approach in which the representation in the Fourier domain of an astronomical source is learned implicitly using a neural field representation. Data-driven priors can be added through a transformer encoder. Results on synthetically observed galaxies show that transformer-conditioned neural fields can successfully reconstruct astronomical observations even when the number of visibilities is very sparse.

Bayesian Imaging with Data-Driven Priors Encoded by Neural Networks

This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis, we adopt a data-driven prior that is supported on a submanifold of the ambient space, which we can learn from the training data using a generative model, such as a variational autoencoder or generative adversarial network. We establish the existence and well-posedness of the associated posterior distribution and posterior moments under easily verifiable conditions, providing a rigorous underpinning for Bayesian estimators and uncertainty quantification analyses. Bayesian computation is performed using a parallel tempered version of the pCN algorithm on the manifold, which is shown to be ergodic and robust to the nonconvex nature of these data-driven models. In addition to point estimators and uncertainty quantification analyses, we derive a model misspecification test to automatically detect situations where the data-driven prior is unreliable, and we explain how to identify the dimension of the latent space directly from the training data. The proposed approach is illustrated with a range of experiments with the MNIST dataset and is compared with some variational and message passing image reconstruction approaches from the state of the art that also use data-driven regularization. A model accuracy analysis suggests that the Bayesian probabilities reported by the proposed data-driven models are also accurate under a frequentist definition of probability, suggesting that the learnt prior is close to the true marginal distribution of the unknown image.

Target temperature management following cardiac arrest: a systematic review and Bayesian meta-analysis

BackgroundTemperature control with target temperature management (TTM) after cardiac arrest has been endorsed by expert societies and adopted in international clinical practice guidelines but recent evidence challenges the use of hypothermic TTM.MethodsSystematic review and Bayesian meta-analysis of clinical trials on adult survivors from cardiac arrest undergoing TTM for at least 12 h comparing TTM versus no TTM or with a separation > 2 °C between intervention and control groups using the PubMed/MEDLINE, EMBASE, CENTRAL databases from inception to 1 September 2021 (PROSPERO CRD42021248140). All randomised and quasi-randomised controlled trials were considered. The risk ratio and 95% confidence interval for death (primary outcome) and unfavourable neurological recovery (secondary outcome) were captured using the original study definitions censored up to 180 days after cardiac arrest. Bias was assessed using the updated Cochrane risk-of-bias for randomised trials tool and certainty of evidence assessed using the Grading of Recommendation Assessment, Development and Evaluation methodology. A hierarchical robust Bayesian model-averaged meta-analysis was performed using both minimally informative and data-driven priors and reported by mean risk ratio (RR) and its 95% credible interval (95% CrI).ResultsIn seven studies (three low bias, three intermediate bias, one high bias, very low to low certainty) recruiting 3792 patients the RR by TTM 32–34 °C was 0.95 [95% CrI 0.78—1.09] for death and RR 0.93 [95% CrI 0.84—1.02] for unfavourable neurological outcome. The posterior probability for no benefit (RR ≥ 1) by TTM 32–34 °C was 24% for death and 12% for unfavourable neurological outcome. The posterior probabilities for favourable treatment effects of TTM 32–34 °C were the highest for an absolute risk reduction of 2–4% for death (28–53% chance) and unfavourable neurological outcome (63–78% chance). Excluding four studies without active avoidance of fever in the control arm reduced the probability to achieve an absolute risk reduction > 2% for death or unfavourable neurological outcome to ≤ 50%.ConclusionsThe posterior probability distributions did not support the use of TTM at 32–34 °C compared to 36 °C also including active control of fever to reduce the risk of death and unfavourable neurological outcome at 90–180 days. Any likely benefit of hypothermic TTM is smaller than targeted in RCTs to date.

Hyperspectral Denoising Using Unsupervised Disentangled Spatiospectral Deep Priors

Image denoising is often empowered by accurate prior information. In recent years, data-driven neural network priors have shown promising performance for RGB natural image denoising. Compared to classic handcrafted priors (e.g., sparsity and total variation), the "deep priors" are learned using a large number of training samples -- which can accurately model the complex image generating process. However, data-driven priors are hard to acquire for hyperspectral images (HSIs) due to the lack of training data. A remedy is to use the so-called unsupervised deep image prior (DIP). Under the unsupervised DIP framework, it is hypothesized and empirically demonstrated that proper neural network structures are reasonable priors of certain types of images, and the network weights can be learned without training data. Nonetheless, the most effective unsupervised DIP structures were proposed for natural images instead of HSIs. The performance of unsupervised DIP-based HSI denoising is limited by a couple of serious challenges, namely, network structure design and network complexity. This work puts forth an unsupervised DIP framework that is based on the classic spatio-spectral decomposition of HSIs. Utilizing the so-called linear mixture model of HSIs, two types of unsupervised DIPs, i.e., U-Net-like network and fully-connected networks, are employed to model the abundance maps and endmembers contained in the HSIs, respectively. This way, empirically validated unsupervised DIP structures for natural images can be easily incorporated for HSI denoising. Besides, the decomposition also substantially reduces network complexity. An efficient alternating optimization algorithm is proposed to handle the formulated denoising problem. Semi-real and real data experiments are employed to showcase the effectiveness of the proposed approach.