BUQO
swMATH ID:  34653 
Software Authors:  Repetti, Audrey; Pereyra, Marcelo; Wiaux, Yves 
Description:  Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization. We propose a Bayesian uncertainty quantification method for largescale imaging inverse problems. Our method applies to all Bayesian models that are logconcave, where maximum a posteriori (MAP) estimation is a convex optimization problem. The method is a framework to analyze the confidence in specific structures observed in MAP estimates (e.g., lesions in medical imaging, celestial sources in astronomical imaging), to enable using them as evidence to inform decisions and conclusions. Precisely, following Bayesian decision theory, we seek to assert the structures under scrutiny by performing a Bayesian hypothesis test that proceeds as follows: first, it postulates that the structures are not present in the true image, and then seeks to use the data and prior knowledge to reject this null hypothesis with high probability. Computing such tests for imaging problems is generally very difficult because of the high dimensionality involved. A main feature of this work is to leverage probability concentration phenomena and the underlying convex geometry to formulate the Bayesian hypothesis test as a convex problem, which we then efficiently solve by using scalable optimization algorithms. This allows scaling to highresolution and highsensitivity imaging problems that are computationally unaffordable for other Bayesian computation approaches. We illustrate our methodology, dubbed BUQO (Bayesian Uncertainty Quantification by Optimization), on a range of challenging Fourier imaging problems arising in astronomy and medicine. MATLAB code for the proposed uncertainty quantification method is available on GitHub. 
Homepage:  https://baspgroup.github.io/BUQO/ 
Source Code:  https://github.com/baspgroup/BUQO 
Dependencies:  Matlab 
Keywords:  Bayesian inference; uncertainty quantification; hypothesis testing; inverse problems; convex optimization; image processing 
Related Software:  BSDS; UNLocBoX; FFDNet; PRMLT; DnCNN; SPIRAL; BayesDA; GMRFLib; FieldTrip; FEAPpv; glasso; fda (R); RRR; SROCK; GitHub; Matlab; Wasserstein GAN; DeepAdverserialRegulariser; NETT; DGM 
Cited in:  6 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization. Zbl 1429.94022 Repetti, Audrey; Pereyra, Marcelo; Wiaux, Yves 
2019

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Cited by 19 Authors
Cited in 3 Serials
4  SIAM Journal on Imaging Sciences 
1  Inverse Problems 
1  Acta Numerica 
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