Sparsity-promoting and edge-preserving maximum
                    <i>a posteriori</i>
                    estimators in non-parametric Bayesian inverse problems

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

doi:10.1088/1361-6420/aaacac

Cited by 45 publications

(92 citation statements)

References 78 publications

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“…Recent results however provide a good characterization in many relevant cases (cf. [209,268,2] ). A relation between Bayesian estimators and the variational approach also exists beyond the MAP estimate by the Bayes cost method.…”

Section: Variational Modelingmentioning

confidence: 99%

Modern regularization methods for inverse problems

2018

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Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards nonlinear regularization methods even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this development towards modern nonlinear regularization methods, including their analysis, applications, and issues for future research.In particular we will discuss variational methods and techniques derived from those, since they have attracted particular interest in the last years and link to other fields like image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions, and learning theory.

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Section: Variational Modelingmentioning

confidence: 99%

Modern regularization methods for inverse problems

2018

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“…Under appropriate conditions, E α,β t (·; f ) can be interpreted as the Onsager-Machlup functional of a posterior distribution and its minimizer is the maximum a-posteriori probability (MAP) estimate (cf. [21,22]). In the finite-dimensional case the posterior density is often simply modeled as p(u|f ) ∼ exp(−cE α,β one usually chooses β = 1 based on the standard formulation of the variational problem.…”

Section: Relation Of the Problemsmentioning

confidence: 99%

Solution paths of variational regularization methods for inverse problems

Bungert

Burger

2019

Inverse Problems

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We consider a family of variational regularization functionals for a generic inverse problem, where the data fidelity and regularization term are given by powers of a Hilbert norm and an absolutely one-homogeneous functional, respectively. We investigate the small and large time behavior of the associated solution paths and, in particular, prove finite extinction time for a large class of functionals. Depending on the powers, we also show that the solution paths are of bounded variation or even Lipschitz continuous. In addition, it will turn out that the models are "almost" mutually equivalent in terms of the minimizers they admit. Finally, we apply our results to define and compare two different nonlinear spectral representations of data and show that only one of it is able to decompose a linear combination of nonlinear eigenvectors into the individual eigenvectors. Finally, we also briefly address piecewise affine solution paths.

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“…Higher order crossings, Wavelet transform, Moment invariant [85], [86], [87], [88] [89] which uses a Bayesian approach. The perception of updating probabilities in the Bayesian method needs a density or probability distribution for the parameters prior to data observation.…”

Section: )mentioning

confidence: 99%

Pattern Mining Approaches Used in Sensor-Based Biometric Recognition: A Review

et al. 2019

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Sensing technologies place significant interest in the use of biometrics for the recognition and assessment of individuals. Pattern mining techniques have established a critical step in the progress of sensor-based biometric systems that are capable of perceiving, recognizing and computing sensor data, being a technology that searches for the high-level information about pattern recognition from low-level sensor readings in order to construct an artificial substitute for human recognition. The design of a successful sensor-based biometric recognition system needs to pay attention to the different issues involved in processing variable data being-acquisition of biometric data from a sensor, data pre-processing, feature extraction, recognition and/or classification, clustering and validation. A significant number of approaches from image processing, pattern identification and machine learning have been used to process sensor data. This paper aims to deliver a state-of-the-art summary and present strategies for utilizing the broadly utilized pattern mining methods in order to identify the challenges as well as future research directions of sensor-based biometric systems.

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Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

Cited by 45 publications

References 78 publications

Modern regularization methods for inverse problems

Modern regularization methods for inverse problems

Solution paths of variational regularization methods for inverse problems

Pattern Mining Approaches Used in Sensor-Based Biometric Recognition: A Review

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