Expectation propagation for Poisson data

Zhang, Chen; Arridge, Simon; Jin, Bangti

doi:10.1088/1361-6420/ab15a3

Cited by 17 publications

(17 citation statements)

References 46 publications

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“…Section 4 provides background information on conditional variational autoencoder, and describes our proposed framework, including the network architecture, and the training and inference phases. In Section 5, we showcase our framework on an established medical imaging modalitypositron emission tomography (PET) [45], for which uncertainty quantification has long been desired yet still very challenging to achieve [54,17,57], and confirm that the generated samples are indeed of high quality in terms of both point estimation and uncertainty quantification, when compared with several state-of-the-art benchmarks. Finally, in Section 6, we conclude the paper with additional discussions.…”

Section: Introductionmentioning

confidence: 76%

Conditional Introspective Variational Autoencoder for Image Synthesis

et al. 2020

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We present a variational autoencoder (VAE) learning framework with introspective training for conditional image synthesis, and explore conditional capsule encoder by class-wise mask label insertion for this framework. Our model only consists of encoder (E), generator (G) and classifier (C), where E and G can be adversarially optimized, and C helps to boost conditional generation, improve authenticity and provide generation measures for E and G. Discriminator is not necessary in our framework and its absence makes our model more concise with fewer artifacts and pattern collapse problems. To compensate for the blurry weakness of VAE-like models, feature matching is introduced into loss functions by means of C to offer more reasonable measures between real and synthesized images. Moreover, in consideration of the key role of E in autoencoders as well as the interesting characteristics of capsule structure, conditional capsule encoder is preliminary explored in the image synthesis model. Class labels participate conditional encoding by masking high-level capsules of other categories, and capsule loss for the encoder is added to facilitate conditional synthesis. Experiments on MNIST and Fashion-MNIST data sets show that our model achieves real conditional synthesis performances with better diversity and fewer artifacts. And conditional capsule encoder also reveals interesting synthesis effects.

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Section: Introductionmentioning

confidence: 76%

Conditional Introspective Variational Autoencoder for Image Synthesis

et al. 2020

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“…Section 4 provides background information on the conditional variational autoencoder and describes our proposed framework, including the network architecture and the training and inference phases. In Section 5, we showcase our framework on an established medical imaging modalitypositron emission tomography (PET) [28]-for which uncertainty quantification has long been desired yet is still very challenging to achieve [29][30][31], and confirm that the generated samples are indeed of high quality in terms of both point estimation and uncertainty quantification when compared with several state-of-the-art benchmarks. Finally, in Section 6, we conclude the paper with additional discussions.…”

Section: Introductionmentioning

confidence: 78%

“…More recently, learning-based approaches have been proposed. While these techniques have been successful, they still lack the capability to provide uncertainty estimates; see the work of [29][30][31]37] for several recent studies on UQ in PET reconstruction, although none of them is based on deep learning.…”

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

“…In the machine learning community, there is a myriad of different ways to approximate a target distribution using an approximate inference scheme, e.g., variational inference [35], variational Gaussian [36,37], expectation propagation [26,29], and Laplace approximation [38]. This work provides one way to approximate the distribution using cVAE.…”

Section: Related Workmentioning

confidence: 99%

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Conditional Variational Autoencoder for Learned Image Reconstruction

2021

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Learned image reconstruction techniques using deep neural networks have recently gained popularity and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect information uncertainty. In this work, we develop a novel computational framework that approximates the posterior distribution of the unknown image at each query observation. The proposed framework is very flexible: it handles implicit noise models and priors, it incorporates the data formation process (i.e., the forward operator), and the learned reconstructive properties are transferable between different datasets. Once the network is trained using the conditional variational autoencoder loss, it provides a computationally efficient sampler for the approximate posterior distribution via feed-forward propagation, and the summarizing statistics of the generated samples are used for both point-estimation and uncertainty quantification. We illustrate the proposed framework with extensive numerical experiments on positron emission tomography (with both moderate and low-count levels) showing that the framework generates high-quality samples when compared with state-of-the-art methods.

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“…Since the seminal work of Vardi, Shepp, and Kaufman (1985), Vardi and Lee (1993), Fredholm equations have also been widely used in positron emission tomography. In this and similar contexts, f corresponds to an image which needs to be inferred from noisy measurements (Snyder, Schulz, and O'Sullivan 1992;Aster, Borchers, and Thurber 2018;Clason, Kaltenbacher, and Resmerita 2019;Zhang, Arridge, and Jin 2019).…”

Section: Introductionmentioning

confidence: 99%

A Particle Method for Solving Fredholm Equations of the First Kind

Crucinio

Doucet

Johansen

2021

Journal of the American Statistical Association

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Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear in instrumental variable regression. However, their numerical solution remains a challenging problem. Many techniques currently available require a preliminary discretization of the domain of the solution and make strong assumptions about its regularity. For example, the popular expectation-maximization smoothing (EMS) scheme requires the assumption of piecewise constant solutions which is inappropriate for most applications. We propose here a novel particle method that circumvents these two issues. This algorithm can be thought of as a Monte Carlo approximation of the EMS scheme which not only performs an adaptive stochastic discretization of the domain but also results in smooth approximate solutions. We analyze the theoretical properties of the EMS iteration and of the corresponding particle algorithm. Compared to standard EMS, we show experimentally that our novel particle method provides state-of-the-art performance for realistic systems, including motion deblurring and reconstruction of cross-sectional images of the brain from positron emission tomography.

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Expectation propagation for Poisson data

Cited by 17 publications

References 46 publications

Conditional Introspective Variational Autoencoder for Image Synthesis

Conditional Introspective Variational Autoencoder for Image Synthesis

Conditional Variational Autoencoder for Learned Image Reconstruction

A Particle Method for Solving Fredholm Equations of the First Kind

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