Pub Date : 2023-12-22DOI: 10.1007/s10851-023-01169-4
Kwancheol Shin, Sanwar Ahmad, Talles Batista Rattis Santos, Nilton Barbosa da Rosa Junior, Jennifer L. Mueller
{"title":"Comparison of Two Linearization-Based Methods for 3-D EIT Reconstructions on a Simulated Chest","authors":"Kwancheol Shin, Sanwar Ahmad, Talles Batista Rattis Santos, Nilton Barbosa da Rosa Junior, Jennifer L. Mueller","doi":"10.1007/s10851-023-01169-4","DOIUrl":"https://doi.org/10.1007/s10851-023-01169-4","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138947475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-15DOI: 10.1007/s10851-023-01168-5
Kexin Sun, Youcai Xu, Minfu Feng
Since MRI is often corrupted by Rician noise, in medical image processing, Rician denoising and deblurring is an important research. In this work, considering the validity of the non-convex log term in the Rician denoising and deblurring model estimated by the maximum a posteriori (MAP) and total variation, we apply nmBDCA to deal with the model. A non-monotonic line search applied in nmBDCA can achieve possible growth of objective function values controlled by parameters. After that, the obtained convex problem is solved separately by alternating direction method of multipliers (ADMM). For (u-)subproblem in ADMM scheme, Caputo fractional derivative and tailored finite point method are applied to denoising, which retain more texture details and suppress the staircase effect. We also demonstrate the convergence of the model and perform the stability analysis on the numerical scheme. Numerical results show that our method can well improve the quality of image restoration.
{"title":"Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring","authors":"Kexin Sun, Youcai Xu, Minfu Feng","doi":"10.1007/s10851-023-01168-5","DOIUrl":"https://doi.org/10.1007/s10851-023-01168-5","url":null,"abstract":"<p>Since MRI is often corrupted by Rician noise, in medical image processing, Rician denoising and deblurring is an important research. In this work, considering the validity of the non-convex log term in the Rician denoising and deblurring model estimated by the maximum a posteriori (MAP) and total variation, we apply nmBDCA to deal with the model. A non-monotonic line search applied in nmBDCA can achieve possible growth of objective function values controlled by parameters. After that, the obtained convex problem is solved separately by alternating direction method of multipliers (ADMM). For <span>(u-)</span>subproblem in ADMM scheme, Caputo fractional derivative and tailored finite point method are applied to denoising, which retain more texture details and suppress the staircase effect. We also demonstrate the convergence of the model and perform the stability analysis on the numerical scheme. Numerical results show that our method can well improve the quality of image restoration.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-03DOI: 10.1007/s10851-023-01167-6
Angelina Senchukova, Jarkko Suuronen, Jere Heikkinen, Lassi Roininen
We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source–detector pair, which creates the issue of unknown geometry. This work considers an approach for geometry estimation based on the calibration object. We parametrise the geometry using a set of 5 parameters. To estimate the geometry parameters, we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The approach allows estimating geometry parameters from full-angle measurements as well as from sparse measurements. We show numerically that different sets of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with first-order isotropic Cauchy difference priors for reconstruction of synthetic and real sawmill data with a very low number of measurements.
{"title":"Geometry Parameter Estimation for Sparse X-Ray Log Imaging","authors":"Angelina Senchukova, Jarkko Suuronen, Jere Heikkinen, Lassi Roininen","doi":"10.1007/s10851-023-01167-6","DOIUrl":"https://doi.org/10.1007/s10851-023-01167-6","url":null,"abstract":"<p>We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source–detector pair, which creates the issue of unknown geometry. This work considers an approach for geometry estimation based on the calibration object. We parametrise the geometry using a set of 5 parameters. To estimate the geometry parameters, we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The approach allows estimating geometry parameters from full-angle measurements as well as from sparse measurements. We show numerically that different sets of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with first-order isotropic Cauchy difference priors for reconstruction of synthetic and real sawmill data with a very low number of measurements.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1007/s10851-023-01162-x
Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt
Abstract Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family generative regularisers . The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results. Finally, we discuss future directions and open problems in the field.
{"title":"Regularising Inverse Problems with Generative Machine Learning Models","authors":"Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt","doi":"10.1007/s10851-023-01162-x","DOIUrl":"https://doi.org/10.1007/s10851-023-01162-x","url":null,"abstract":"Abstract Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family generative regularisers . The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results. Finally, we discuss future directions and open problems in the field.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-28DOI: 10.1007/s10851-023-01163-w
Yann Traonmilin, Jean-François Aujol, Pierre-Jean Bénard, Arthur Leclaire
{"title":"On Strong Basins of Attractions for Non-convex Sparse Spike Estimation: Upper and Lower Bounds","authors":"Yann Traonmilin, Jean-François Aujol, Pierre-Jean Bénard, Arthur Leclaire","doi":"10.1007/s10851-023-01163-w","DOIUrl":"https://doi.org/10.1007/s10851-023-01163-w","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135386446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-19DOI: 10.1007/s10851-023-01164-9
Michael Q. Rieck
{"title":"Geometric Conditions for the Existence or Non-existence of a Solution to the Perspective 3-Point Problem","authors":"Michael Q. Rieck","doi":"10.1007/s10851-023-01164-9","DOIUrl":"https://doi.org/10.1007/s10851-023-01164-9","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135063177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-16DOI: 10.1007/s10851-023-01154-x
Nicolas Passat, Julien Mendes Forte, Y. Kenmochi
{"title":"Morphological Hierarchies: A Unifying Framework with New Trees","authors":"Nicolas Passat, Julien Mendes Forte, Y. Kenmochi","doi":"10.1007/s10851-023-01154-x","DOIUrl":"https://doi.org/10.1007/s10851-023-01154-x","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45426412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-16DOI: 10.1007/s10851-023-01156-9
F. Belém, I. B. Barcelos, L. Joao, B. Perret, J. Cousty, S. Guimarães, A. Falcão
{"title":"Novel Arc-Cost Functions and Seed Relevance Estimations for Compact and Accurate Superpixels","authors":"F. Belém, I. B. Barcelos, L. Joao, B. Perret, J. Cousty, S. Guimarães, A. Falcão","doi":"10.1007/s10851-023-01156-9","DOIUrl":"https://doi.org/10.1007/s10851-023-01156-9","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47925933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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