ArticleEntropy (Basel, Switzerland)2021
Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems.
Article in Entropy (Basel, Switzerland), 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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8 citing papers in PubMed.
- Probabilistic nested model selection in pharmacokinetic analysis of DCE-MRI data in animal model of cerebral tumor.Scientific reports · 2025Article
- The Second Law of Infodynamics: A Thermocontextual Reformulation.Entropy (Basel, Switzerland) · 2024Article
- Probabilistic Nested Model Selection in Pharmacokinetic Analysis of DCE-MRI Data in Animal Model of Cerebral Tumor.Research square · 2024Article
- Dynamic contrast enhanced (DCE) MRI estimation of vascular parameters using knowledge-based adaptive models.Scientific reports · 2023Article
- Machine-Learning-Based Data Analysis Method for Cell-Based Selection of DNA-Encoded Libraries.ACS omega · 2023Article
- Quantitative assessment method of muzzle flash and smoke at high noise level on field environment.Scientific reports · 2023Article
- Programmable Density of Laser Additive Manufactured Parts by Considering an Inverse Problem.Materials (Basel, Switzerland) · 2022Article
- Computational Methods for Parameter Identification in 2D Fractional System with Riemann-Liouville Derivative.Sensors (Basel, Switzerland) · 2022Article
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Abstract
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion.
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