Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior
| Autor: | Mario González, Andrés Almansa, Pauline Tan |
|---|---|
| Přispěvatelé: | Universidad de la República (UDELAR), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), ANR-19-CE23-0027,PostProdLEAP,Repenser la post-production d'archives avec des méthodes à patch, variationnelles et par apprentissage(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Bi-convex Optimization Computer Science - Machine Learning General Mathematics Computer Vision and Pattern Recognition (cs.CV) Inverse Problems Computer Science - Computer Vision and Pattern Recognition Machine Learning (stat.ML) Machine Learning (cs.LG) [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Statistics - Machine Learning FOS: Electrical engineering electronic engineering information engineering FOS: Mathematics Generative Models Image Restoration Variational Auto-encoders Mathematics - Optimization and Control Applied Mathematics Image and Video Processing (eess.IV) Electrical Engineering and Systems Science - Image and Video Processing Optimization and Control (math.OC) [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Bayesian Statistics [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Popis: | In this work we address the problem of solving ill-posed inverse problems in imaging where the prior is a variational autoencoder (VAE). Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique (JPMAP) performs Joint Posterior Maximization using an Autoencoding Prior. We show theoretical and experimental evidence that the proposed objective function is quite close to bi-convex. Indeed it satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. We also highlight the importance of correctly training the VAE using a denoising criterion, in order to ensure that the encoder generalizes well to out-of-distribution images, without affecting the quality of the generative model. This simple modification is key to providing robustness to the whole procedure. Finally we show how our joint MAP methodology relates to more common MAP approaches, and we propose a continuation scheme that makes use of our JPMAP algorithm to provide more robust MAP estimates. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima. Comment: arXiv admin note: text overlap with arXiv:1911.06379 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|