2021
DOI: 10.20944/preprints202111.0092.v1
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Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†

Abstract: Classical methods for inverse problems are mainly based on regularization theory. In particular those which 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 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, respectively, to the likelihood and prio… Show more

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Cited by 12 publications
(5 citation statements)
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“…Previously, Lim and co-workers reported a maximum-likelihood enrichment calculation method rooted in the ratio testing of two Poisson rates reported, 64 since the next-generation sequencing data of DEL selections corresponds well with a Poisson distribution. 53,89 Inspired by this work, we applied Maximum A Posteriori estimation, a Bayesian-inference-based method that has been proven to be effective in processing noisy and uncertain datasets, 90 to denoise the cell-based selection data. The ratio of two Poisson rates (R) can be modeled by a common exponential prior density distribution (eq.…”
Section: Resultsmentioning
confidence: 99%
“…Previously, Lim and co-workers reported a maximum-likelihood enrichment calculation method rooted in the ratio testing of two Poisson rates reported, 64 since the next-generation sequencing data of DEL selections corresponds well with a Poisson distribution. 53,89 Inspired by this work, we applied Maximum A Posteriori estimation, a Bayesian-inference-based method that has been proven to be effective in processing noisy and uncertain datasets, 90 to denoise the cell-based selection data. The ratio of two Poisson rates (R) can be modeled by a common exponential prior density distribution (eq.…”
Section: Resultsmentioning
confidence: 99%
“…Although in‐loop hardware‐software design is comparatively sluggish compared to computational practices, the primary challenge in computational imaging lies in computational techniques. Particularly, there are primarily two approaches for solving inverse problems [ 45 ] : classical optimization and neural network‐based algorithms, each with its own advantages and disadvantages. Classical optimization algorithms.…”
Section: Differentiable Imagingmentioning
confidence: 99%
“…The AMs that have been constructed can serve as flexible predictors in that they can be re-trained and finetuned based on different optimization methods such as standard NLS fitting, regularized Bayesian estimation methods 72 , etc. Due to their strong generalizability, they can provide high tolerance and robustness against low signal-to-noise, contrast-to-noise ratios, and potential outliers.…”
Section: In Recent Years Studies Have Investigated the Development Of...mentioning
confidence: 99%