The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without employing sparsity at all. Instead, we suppose that vectors lie near the range of a generative model G : R k → R n . Our main theorem is that, if G is L-Lipschitz, then roughly O(k log L) random Gaussian measurements suffice for an 2/ 2 recovery guarantee. We demonstrate our results using generative models from published variational autoencoder and generative adversarial networks. Our method can use 5-10x fewer measurements than Lasso for the same accuracy.
Background Diabetic retinopathy screening is instrumental to preventing blindness, but scaling up screening is challenging because of the increasing number of patients with all forms of diabetes. We aimed to create a deep-learning system to predict the risk of patients with diabetes developing diabetic retinopathy within 2 years. MethodsWe created and validated two versions of a deep-learning system to predict the development of diabetic retinopathy in patients with diabetes who had had teleretinal diabetic retinopathy screening in a primary care setting. The input for the two versions was either a set of three-field or one-field colour fundus photographs. Of the 575 431 eyes in the development set 28 899 had known outcomes, with the remaining 546 532 eyes used to augment the training process via multitask learning. Validation was done on one eye (selected at random) per patient from two datasets: an internal validation (from EyePACS, a teleretinal screening service in the USA) set of 3678 eyes with known outcomes and an external validation (from Thailand) set of 2345 eyes with known outcomes. Findings The three-field deep-learning system had an area under the receiver operating characteristic curve (AUC) of 0•79 (95% CI 0•77-0•81) in the internal validation set. Assessment of the external validation set-which contained only one-field colour fundus photographs-with the one-field deep-learning system gave an AUC of 0•70 (0•67-0•74). In the internal validation set, the AUC of available risk factors was 0•72 (0•68-0•76), which improved to 0•81 (0•77-0•84) after combining the deep-learning system with these risk factors (p<0•0001). In the external validation set, the corresponding AUC improved from 0•62 (0•58-0•66) to 0•71 (0•68-0•75; p<0•0001) following the addition of the deep-learning system to available risk factors.Interpretation The deep-learning systems predicted diabetic retinopathy development using colour fundus photographs, and the systems were independent of and more informative than available risk factors. Such a risk stratification tool might help to optimise screening intervals to reduce costs while improving vision-related outcomes.Funding Google.
Purpose: To develop and validate a deep learning (DL) algorithm that predicts referable glaucomatous optic neuropathy (GON) and optic nerve head (ONH) features from color fundus images, to determine the relative importance of these features in referral decisions by glaucoma specialists (GSs) and the algorithm, and to compare the performance of the algorithm with eye care providers.Design: Development and validation of an algorithm.Participants: Fundus images from screening programs, studies, and a glaucoma clinic. Methods: A DL algorithm was trained using a retrospective dataset of 86 618 images, assessed for glaucomatous ONH features and referable GON (defined as ONH appearance worrisome enough to justify referral for comprehensive examination) by 43 graders. The algorithm was validated using 3 datasets: dataset A (1205 images, 1 image/patient; 18.1% referable), images adjudicated by panels of GSs; dataset B (9642 images, 1 image/ patient; 9.2% referable), images from a diabetic teleretinal screening program; and dataset C (346 images, 1 image/patient; 81.7% referable), images from a glaucoma clinic.Main Outcome Measures: The algorithm was evaluated using the area under the receiver operating characteristic curve (AUC), sensitivity, and specificity for referable GON and glaucomatous ONH features.Results: The algorithm's AUC for referable GON was 0.945 (95% confidence interval [CI], 0.929e0.960) in dataset A, 0.855 (95% CI, 0.841e0.870) in dataset B, and 0.881 (95% CI, 0.838e0.918) in dataset C. Algorithm AUCs ranged between 0.661 and 0.973 for glaucomatous ONH features. The algorithm showed significantly higher sensitivity than 7 of 10 graders not involved in determining the reference standard, including 2 of 3 GSs, and showed higher specificity than 3 graders (including 1 GS), while remaining comparable to others. For both GSs and the algorithm, the most crucial features related to referable GON were: presence of vertical cup-to-disc ratio of 0.7 or more, neuroretinal rim notching, retinal nerve fiber layer defect, and bared circumlinear vessels.Conclusions: A DL algorithm trained on fundus images alone can detect referable GON with higher sensitivity than and comparable specificity to eye care providers. The algorithm maintained good performance on an independent dataset with diagnoses based on a full glaucoma workup.
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