This paper explores the recently proposed Graph Convolutional Network architecture proposed in (Kipf & Welling, 2016) The key points of their work is summarized and their results are reproduced. Graph regularization and alternative graph convolution approaches are explored. I find that explicit graph regularization was correctly rejected by (Kipf & Welling, 2016). I attempt to improve the performance of GCN by approximating a k-step transition matrix in place of the normalized graph laplacian, but I fail to find positive results. Nonetheless, the performance of several configurations of this GCN variation is shown for the Cora, Citeseer, and Pubmed datasets.
Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a \textit{mathematical connection between graph convolution and graph-regularized PCA} (GPCA). Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking GPCA. We empirically demonstrate that the \textit{unsupervised} embeddings by GPCA paired with a 1- or 2-layer MLP achieves similar or even better performance than GCN on semi-supe…
We propose an unsupervised superpixel segmentation method by optimizing a randomly-initialized convolutional neural network (CNN) in inference time. Our method generates superpixels via CNN from a single image without any labels by minimizing a proposed objective function for superpixel segmentation in inference time. There are three advantages to our method compared with many of existing methods: (i) leverages an image prior of CNN for superpixel segmentation, (ii) adaptively changes the number of superpixels according to the given images, and (iii) controls the property of superpixels by add…
Bigo Inc.（Bigo公司）；Beihang University（北京航空航天大学）；IBM China CIC（IBM中国创新中心）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
We present a probabilistic forecasting framework based on convolutional neural network for multiple related time series forecasting. The framework can be applied to estimate probability density under both parametric and non-parametric settings. More specifically, stacked residual blocks based on dilated causal convolutional nets are constructed to capture the temporal dependencies of the series. Combined with representation learning, our approach is able to learn complex patterns such as seasonality, holiday effects within and across series, and to leverage those patterns for more accurate for…
Inria Saclay（法国国家信息与自动化研究所萨克莱分所）；Univ. Paris Saclay（巴黎萨克雷大学）；IIIT - Delhi（德里英迪拉·甘地信息技术学院）
Co-administration of two or more drugs simultaneously can result in adverse drug reactions. Identifying drug-drug interactions (DDIs) is necessary, especially for drug development and for repurposing old drugs. DDI prediction can be viewed as a matrix completion task, for which matrix factorization (MF) appears as a suitable solution. This paper presents a novel Graph Regularized Probabilistic Matrix Factorization (GRPMF) method, which incorporates expert knowledge through a novel graph-based regularization strategy within an MF framework. An efficient and sounded optimization algorithm is pro…
In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected. The Graph Neural Network (GNN) has proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying gr…
In this paper, we propose a novel progressive parameter pruning method for Convolutional Neural Network acceleration, named Structured Probabilistic Pruning (SPP), which effectively prunes weights of convolutional layers in a probabilistic manner. Unlike existing deterministic pruning approaches, where unimportant weights are permanently eliminated, SPP introduces a pruning probability for each weight, and pruning is guided by sampling from the pruning probabilities. A mechanism is designed to increase and decrease pruning probabilities based on importance criteria in the training process. Exp…
Systems Design Engineering & Center for Theoretical Neuroscience University of Waterloo（滑铁卢大学系统设计工程与理论神经科学中心）；School of Engineering, University of Guelph（圭尔夫大学工程学院）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；Canadian Institute for Advanced Research（加拿大高级研究学院）；University of Guelph（圭尔夫大学）；University of Waterloo（滑铁卢大学）
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of correlated variability, we implement and evaluate correlated noise models in deep convolutional neural networks. Inspired by the cortex, correlation is defined as a function of the distance between neurons and their selectivity. We show how to sample from high-dimensional correlated distributions while keeping the procedure differentiable, so that back-propagation ca…
Machine Learning on graph-structured data is an important and omnipresent task for a vast variety of applications including anomaly detection and dynamic network analysis. In this paper, a deep generative model is introduced to capture continuous probability densities corresponding to the nodes of an arbitrary graph. In contrast to all learning formulations in the area of discriminative pattern recognition, we propose a scalable generative optimization/algorithm theoretically proved to capture distributions at the nodes of a graph. Our model is able to generate samples from the probability den…
Toyota Central R&D LABS., inc.（丰田中央研发实验室股份有限公司）；Frontier Research Center, Toyota Motor Corporation（丰田汽车公司前沿研究中心）；Graduate School of Informatics, Kyoto University（京都大学信息学研究科）
The demand for resilient logistics networks has increased because of recent disasters. When we consider optimization problems, entropy regularization is a powerful tool for the diversification of a solution. In this study, we proposed a method for designing a resilient logistics network based on entropy regularization. Moreover, we proposed a method for analytical resilience criteria to reduce the ambiguity of resilience. First, we modeled the logistics network, including factories, distribution bases, and sales outlets in an efficient framework using entropy regularization. Next, we formulate…
University of California, Irvine（加州大学欧文分校）；Whittier College（惠蒂尔学院）；Qualcomm AI（高通人工智能）
Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group sparsity onto the weights of the layers during the training process, a compressed network can be obtained with accuracy comparable to a dense one. In this paper, we propose a new variant of sparse group lasso that blends the $\ell_0$ norm onto the individual weight parameters and the $\ell_{2,1}$ norm onto the output channels of a layer. To address the non-di…
The combination of a CNN detector and a search framework forms the basis for local object/pattern detection. To handle the waste of regional information and the defective compromise between efficiency and accuracy, this paper proposes a probabilistic model with a powerful search framework. By mapping an image into a probabilistic distribution of objects, this new model gives more informative outputs with less computation. The setting and analytic traits are elaborated in this paper, followed by a series of experiments carried out on FDDB, which show that the proposed model is sound, efficient …
As the number of heterogenous IP-connected devices and traffic volume increase, so does the potential for security breaches. The undetected exploitation of these breaches can bring severe cybersecurity and privacy risks. Anomaly-based \acp{IDS} play an essential role in network security. In this paper, we present a practical unsupervised anomaly-based deep learning detection system called ARCADE (Adversarially Regularized Convolutional Autoencoder for unsupervised network anomaly DEtection). With a convolutional \ac{AE}, ARCADE automatically builds a profile of the normal traffic using a subse…
In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the training objective of an ensemble, derived from the evidence lower bound used in variational inference. We evaluate the uncertainty estimates obtained from our models for active learning on visual classification. Our approach steadily improves upon active learning baselines as the annotation budget is increased.
Qualcomm AI Research（高通人工智能研究院）；New York University（纽约大学）
Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved regions of the input. Drawing from the work in probabilistic numerics, we propose Probabilistic Numeric Convolutional Neural Networks which represent features as Gaussian processes (GPs), providing a probabilistic description of discretization error. We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity…
This paper describes a neural drum transcription method that detects from music signals the onset times of drums at the $\textit{tatum}$ level, where tatum times are assumed to be estimated in advance. In conventional studies on drum transcription, deep neural networks (DNNs) have often been used to take a music spectrogram as input and estimate the onset times of drums at the $\textit{frame}$ level. The major problem with such frame-to-frame DNNs, however, is that the estimated onset times do not often conform with the typical tatum-level patterns appearing in symbolic drum scores because the…
University of Maryland, College Park（马里兰大学帕克分校）；Tsinghua University（清华大学）；Shanghai Qi Zhi Institute（上海期智研究院）
Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics- and learned dynamics-induced Bellman operators is, thus enabling the converged value function …
A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images, and excellent classification results are obtained on the MNIST and Caltech 101 datasets.
Université Bourgogne Franche-Comté（弗朗什-孔泰大学）；UTBM（贝尔福-蒙贝利亚技术大学）；Université de Lorraine（洛林大学）；LORIA（洛林计算机科学与应用实验室）；CNRS（法国国家科学研究中心）
Predicting smartphone users location with WiFi fingerprints has been a popular research topic recently. In this work, we propose two novel deep learning-based models, the convolutional mixture density recurrent neural network and the VAE-based semi-supervised learning model. The convolutional mixture density recurrent neural network is designed for path prediction, in which the advantages of convolutional neural networks, recurrent neural networks and mixture density networks are combined. Further, since most of real-world datasets are not labeled, we devise the VAE-based model for the semi-su…
This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz…
The Institute of Cancer Research（癌症研究院）；University College London（伦敦大学学院）
In digital pathology, cell detection and classification are often prerequisites to quantify cell abundance and explore tissue spatial heterogeneity. However, these tasks are particularly challenging for multiplex immunohistochemistry (mIHC) images due to high levels of variability in staining, expression intensity, and inherent noise as a result of preprocessing artefacts. We proposed a deep learning method to detect and classify cells in mIHC whole-tumour slide images of breast cancer. Inspired by inception-v3, we developed Cell COunt RegularizeD Convolutional neural Network (ConCORDe-Net) wh…
Separation of competing speech is a key challenge in signal processing and a feat routinely performed by the human auditory brain. A long standing benchmark of the spectrogram approach to source separation is known as the ideal binary mask. Here, we train a convolutional deep neural network, on a two-speaker cocktail party problem, to make probabilistic predictions about binary masks. Our results approach ideal binary mask performance, illustrating that relatively simple deep neural networks are capable of robust binary mask prediction. We also illustrate the trade-off between prediction stati…
KTH Royal Institute of Technology（瑞典皇家理工学院）；MessageBird（MessageBird公司）；University of Washington（华盛顿大学）
Sum-Product Networks (SPNs) are hierarchical, graphical models that combine benefits of deep learning and probabilistic modeling. SPNs offer unique advantages to applications demanding exact probabilistic inference over high-dimensional, noisy inputs. Yet, compared to convolutional neural nets, they struggle with capturing complex spatial relationships in image data. To alleviate this issue, we introduce Deep Generalized Convolutional Sum-Product Networks (DGC-SPNs), which encode spatial features in a way similar to CNNs, while preserving the validity of the probabilistic SPN model. As opposed…
We describe convolutional deep exponential families (CDEFs) in this paper. CDEFs are built based on deep exponential families, deep probabilistic models that capture the hierarchical dependence between latent variables. CDEFs greatly reduce the number of free parameters by tying the weights of DEFs. Our experiments show that CDEFs are able to uncover time correlations with a small amount of data.
Massachusetts Institute of Technology（麻省理工学院）；Google Research（谷歌研究院）
We study the problem of synthesizing a number of likely future frames from a single input image. In contrast to traditional methods, which have tackled this problem in a deterministic or non-parametric way, we propose a novel approach that models future frames in a probabilistic manner. Our probabilistic model makes it possible for us to sample and synthesize many possible future frames from a single input image. Future frame synthesis is challenging, as it involves low- and high-level image and motion understanding. We propose a novel network structure, namely a Cross Convolutional Network to…
Ensemble manifold based regularized multi-modal graph convolutional network for cognitive ability prediction
Tulane University（杜兰大学）；Xavier University of Louisiana（路易斯安那泽维尔大学）；Georgia State University（佐治亚州立大学）；Georgia Institute of Technology（佐治亚理工学院）；Emory University（埃默里大学）
Royal Netherlands Meteorological Institute (KNMI)（荷兰皇家气象研究所（KNMI））；Utrecht University（乌得勒支大学）
Current statistical post-processing methods for probabilistic weather forecasting are not capable of using full spatial patterns from the numerical weather prediction (NWP) model. In this paper we incorporate spatial wind speed information by using convolutional neural networks (CNNs) and obtain probabilistic wind speed forecasts in the Netherlands for 48 hours ahead, based on KNMI's deterministic Harmonie-Arome NWP model. The probabilistic forecasts from the CNNs are shown to have higher Brier skill scores for medium to higher wind speeds, as well as a better continuous ranked probability sco…
Accurate lake temperature estimation is essential for numerous problems tackled in both hydrological and ecological domains. Nowadays physical models are developed to estimate lake dynamics; however, computations needed for accurate estimation of lake surface temperature can get prohibitively expensive. We propose to aggregate simulations of lake temperature at a certain depth together with a range of meteorological features to probabilistically estimate lake surface temperature. Accordingly, we introduce a spatio-temporal neural network that combines Bayesian recurrent neural networks and Bay…
Lakehead University（湖首大学）；University of Calgary（卡尔加里大学）
Objective: This paper presents an Alzheimer's disease (AD) detection method based on learning structural similarity between Magnetic Resonance Images (MRIs) and representing this similarity as a graph. Methods: We construct the similarity graph using embedded features of the input image (i.e., Non-Demented (ND), Very Mild Demented (VMD), Mild Demented (MD), and Moderated Demented (MDTD)). We experiment and compare different dimension-reduction and clustering algorithms to construct the best similarity graph to capture the similarity between the same class images using the cosine distance as a …
Solar energy is a clean and renewable energy. Photovoltaic (PV) power is an important way to utilize solar energy. Accurate PV power forecast is crucial to the large-scale application of PV power and the stability of electricity grid. This paper proposes a novel method for short-term photovoltaic power forecast using deep convolutional long short-term memory (ConvLSTM) network and kernel density estimation (KDE). In the proposed method, ConvLSTM is used to forecast the future photovoltaic power and KDE is used for estimating the joint probabilistic density function and giving the probabilistic…
Stability and Generalization of lp-Regularized Stochastic Learning for GCN
University of Electronic Science and Technology of China（电子科技大学）；Northwestern Polytechnical University（西北工业大学）；Nanjing Audit University（南京审计大学）；Zhejiang Normal University（浙江师范大学）
School of Computer Science & Informatics, Cardiff University（卡迪夫大学计算机科学与信息学院）
A novel kernel-based support vector machine (SVM) for graph classification is proposed. The SVM feature space mapping consists of a sequence of graph convolutional layers, which generates a vector space representation for each vertex, followed by a pooling layer which generates a reproducing kernel Hilbert space (RKHS) representation for the graph. The use of a RKHS offers the ability to implicitly operate in this space using a kernel function without the computational complexity of explicitly mapping into it. The proposed model is trained in a supervised end-to-end manner whereby the convolut…
Energy-Regularized Spatial Masking: A Novel Approach to Enhancing Robustness and Interpretability in Vision Models
DAVID Lab, UVSQ, Paris-Saclay University（DAVID实验室，UVSQ，巴黎-萨克雷大学）；LIPN, UMR CNRS 7030, Sorbonne Paris Nord University（LIPN，UMR CNRS 7030，索邦巴黎北大学）；LISN, Paris-Saclay University（LISN，巴黎-萨克雷大学）
Indian Institute of Space Science and Technology（印度空间科学与技术研究所）
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of using Laplacian in deriving regularization operators on graphs and its consequent use with spectral GCNN filter designs. In this work, we explore the regularization properties of graph Laplacian and proposed a generalized framework for regularized filter designs in spectral GCNNs. We found that the filters used in many state-of-the-art GCNNs can be derived as a …
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via deconvolutional inference. To speed up this inference, a new statistical approach is proposed to project the top-layer dictionary elements to the data level. Following this, only one layer of deconvolution is required during testing. Experimental results demonstrate powerful capabil…
Cell nuclei detection is a challenging research topic because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic of enduring interest with promising recent success shown by deep learning methods. These methods train Convolutional Neural Networks (CNNs) with a training set of input images and known, labeled nuclei locations. Many such methods are supplemented by spatial or morphological processing. Using a set of canonical cell nuclei shapes, prepared with the help of a…
In this work, we provide a new formulation for Graph Convolutional Neural Networks (GCNNs) for link prediction on graph data that addresses common challenges for biomedical knowledge graphs (KGs). We introduce a regularized attention mechanism to GCNNs that not only improves performance on clean datasets, but also favorably accommodates noise in KGs, a pervasive issue in real-world applications. Further, we explore new visualization methods for interpretable modelling and to illustrate how the learned representation can be exploited to automate dataset denoising. The results are demonstrated o…
A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with both linear and non-linear multivariate probability distributions such as the elliptical and generalized hyperbolic families. It can also be directly implemented for $L_0$-norm regularized multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific $L_0$-norm regularized expectation-ma…
The goal of this study was to improve the post-processing of precipitation forecasts using convolutional neural networks (CNNs). Instead of post-processing forecasts on a per-pixel basis, as is usually done when employing machine learning in meteorological post-processing, input forecast images were combined and transformed into probabilistic output forecast images using fully convolutional neural networks. CNNs did not outperform regularized logistic regression. Additionally, an ablation analysis was performed. Combining input forecasts from a global low-resolution weather model and a regiona…
Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically principled, BNNs require approximations to be applied to large-scale problems, where both performance and uncertainty estimation are crucial. In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep BNN. We conduct a series of large-scale visual active learning experiments t…
Albert Einstein College of Medicine（阿尔伯特·爱因斯坦医学院）；École Normale Supérieure, PSL University（巴黎高等师范学院，巴黎文理研究大学）
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly, it is common to introduce a Laplacian constraint on the posterior probability that each data point belongs to a class. Alternatively, the mixing probabilities can be treated as free parameters, while assuming Gauss-Markov or more complex priors to regularize those mixing probabilities. However, these approaches are constrained by the shape of the prior and of…
Qualcomm AI Research（高通人工智能研究院）；Qualcomm Technologies Netherlands B.V.（高通技术荷兰有限公司）；Qualcomm Technologies, Inc.（高通技术公司）
The success of deep neural networks in many real-world applications is leading to new challenges in building more efficient architectures. One effective way of making networks more efficient is neural network compression. We provide an overview of existing neural network compression methods that can be used to make neural networks more efficient by changing the architecture of the network. First, we introduce a new way to categorize all published compression methods, based on the amount of data and compute needed to make the methods work in practice. These are three 'levels of compression solu…
Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weig…
The Robotics Institute, School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院机器人研究所）；Facebook；Michigan State University（密歇根州立大学）
Feature representations from pre-trained deep neural networks have been known to exhibit excellent generalization and utility across a variety of related tasks. Fine-tuning is by far the simplest and most widely used approach that seeks to exploit and adapt these feature representations to novel tasks with limited data. Despite the effectiveness of fine-tuning, itis often sub-optimal and requires very careful optimization to prevent severe over-fitting to small datasets. The problem of sub-optimality and over-fitting, is due in part to the large number of parameters used in a typical deep conv…
Centrum Wiskunde & Informatica (CWI)（荷兰数学与计算机科学研究中心）；Holst Centre / IMEC（霍尔斯特中心/比利时微电子研究中心）；Technical University Eindhoven（埃因霍温理工大学）；University of Amsterdam（阿姆斯特丹大学）；Rijksuniversiteit Groningen（格罗宁根大学）
While modern convolutional neural networks achieve outstanding accuracy on many image classification tasks, they are, compared to humans, much more sensitive to image degradation. Here, we describe a variant of Batch Normalization, LocalNorm, that regularizes the normalization layer in the spirit of Dropout while dynamically adapting to the local image intensity and contrast at test-time. We show that the resulting deep neural networks are much more resistant to noise-induced image degradation, improving accuracy by up to three times, while achieving the same or slightly better accuracy on non…
Dept. Information Eng., Electronics and Telecomm., Sapienza University of Rome（罗马一大信息工程、电子与电信系）；Dept. Communications Eng., University of Cantabria（坎塔布里亚大学通信工程系）
Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kerne…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this paper is to provide a learning method to compute the most likely relationship between two nodes in a framework based on probabilistic graphs. In particular, given a probabilistic graph we adopted the language-constraint reachability method to compute the probability of possible interconnections that may exists between two nodes. Each of these connections ma…
Convolutional deep neural networks (DNN) are state of the art in many engineering problems but have not yet addressed the issue of how to deal with complex spectrograms. Here, we use circular statistics to provide a convenient probabilistic estimate of spectrogram phase in a complex convolutional DNN. In a typical cocktail party source separation scenario, we trained a convolutional DNN to re-synthesize the complex spectrograms of two source speech signals given a complex spectrogram of the monaural mixture - a discriminative deep transform (DT). We then used this complex convolutional DT to o…
Idiap Research Institute（伊迪亚普研究所）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvo…
