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A Linear Programming Relaxation for Binary Tomography with Smoothness Priors

2003
*
Electronic Notes in Discrete Mathematics
*

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##
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Discrete tomography by convex–concave regularization and D.C. programming

2005
*
Discrete Applied Mathematics
*

*A*quadratic objective functional over

*binary*variables comprising the squared projection error and

*a*

*prior*penalizing non-homogeneous regions, is supplemented

*with*

*a*concave functional enforcing

*binary*... Our approach is applicable to quite general objective functions over

*binary*variables

*with*constraints and thus applicable to

*a*wide range of problems within and beyond the field of discrete

*tomography*... [11] introduced the following

*linear*integer

*programming*problem

*for*

*binary*

*tomography*: and suggested

*a*range of greedy approaches within

*a*general framework

*for*local search. ...

##
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A Linear Programming Approach to Limited Angle 3D Reconstruction from DSA Projections
[chapter]

2003
*
Informatik aktuell
*

*a*

*smoothness*

*prior*. ... Objectives: We investigate the feasibility of

*binary*-valued 3D tomographic reconstruction using only

*a*small number of projections acquired over

*a*limited range of angles. ... Volumegraphics (http://www.volumegraphics.com) kindly provided us

*with*their volume rendering software. All 3D models in this paper were rendered

*with*VGStudioMax 1.1. ...

##
###
Prior Learning and Convex-Concave Regularization of Binary Tomography

2005
*
Electronic Notes in Discrete Mathematics
*

*A*convex reconstruction functional, comprising the projections equations and

*a*

*smoothness*

*prior*, was complemented

*with*

*a*concave penalty term enforcing

*binary*solutions. ... We show that the difference-of-convex-functions DC-

*programming*framework is flexible enough to cope

*with*this more general model class. ...

*Smoothness*

*priors*are convenient from the computational viewpoint because they result in convex functionals having

*relaxed*the

*binary*constraint. ...

##
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TomoGC: Binary Tomography by Constrained GraphCuts
[chapter]

2015
*
Lecture Notes in Computer Science
*

We present an iterative reconstruction algorithm

doi:10.1007/978-3-319-24947-6_21
fatcat:h4yf3qrzxrdkresc3sg7owv6tu
*for**binary**tomography*, called TomoGC, that solves the reconstruction problem based on*a*constrained graphical model by*a*sequence of graphcuts. ...*A*comprehensive numerical evaluation demonstrates that the proposed method can reconstruct objects from*a*small number of projections more accurate and also faster than competitive methods. ... The*relaxed**linear**program*can then have nonbinary solutions. ...##
###
Discrete Tomography by Continuous Multilabeling Subject to Projection Constraints
[chapter]

2016
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-319-45886-1_21
fatcat:i6nzn4fvljcwvfqftz5nm56mnq
*a*non-convex variational approach to non-*binary*discrete*tomography*which combines non-local projection constraints*with**a*continuous convex*relaxation*of the multilabeling problem. ...*A*competitive numerical evaluation using standard test-datasets demonstrates*a*significantly improved reconstruction quality*for*noisy measurements from*a*small number of projections. ... [29, 21] proposed to combine*a*quadratic*program**with**a*non-convex penalty which gradually enforces*binary*constraints. More recently, Kappes et al. ...##
###
Adaptive Reconstruction of Discrete-Valued Objects from few Projections

2005
*
Electronic Notes in Discrete Mathematics
*

Recently, we proposed an algorithm

doi:10.1016/j.endm.2005.05.074
fatcat:uf4sz54zinf67ccqqujtkefh3e
*for**binary**tomography*based on DC ( difference of convex functions )*programming*[13, 15] . ... The proposed algorithm remains practicable*for*multi-valued reconstructions, and even*with**a*large number of discrete values. ...*Binary*Objects Reconstruction Using*a**linear*transformation*for*the projection process of transmission*tomography*, the reconstruction problem becomes an inverse problem*for*Ax = b (1)*with*unknown x ...##
###
Binary Tomography by Iterating Linear Programs from Noisy Projections
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we improve the behavior of

doi:10.1007/978-3-540-30503-3_3
fatcat:dbg2rfeld5f7tjdzh6ir36bn3m
*a*reconstruction algorithm*for**binary**tomography*in the presence of noise. ... The objective function contains*a**smoothness**prior*that favors spatially homogeneous solutions and*a*concave functional gradually enforcing*binary*solutions. ... [7] introduced the following*linear*integer*programming*problem*for**binary**tomography*: max x∈{0,1} n e, x , e := (1, . . . , 1) , Ax ≤ b , (3) and suggested*a*range of greedy approaches within*a*general ...##
###
On image reconstruction algorithms for binary electromagnetic geotomography

2008
*
Theoretical Computer Science
*

The assumption

doi:10.1016/j.tcs.2008.06.007
fatcat:gzecuujwbbh57exaptlmypbs7y
*for**a**binary*representation of the image to be reconstructed substantially*relaxes*image reconstruction problems related to ill-posedness that comes from an intrinsic limitation of an angular ... We test two algorithms*for**binary**tomography*, where the penalty term is based on the Markov Random Field (MRF) model. ... The author is also grateful to the anonymous reviewers*for*their valuable comments and suggestions. ...##
###
Efficient Message Passing for 0-1 ILPs with Binary Decision Diagrams
[article]

2021
*
arXiv
*
pre-print

We present

arXiv:2009.00481v2
fatcat:aq3kyrwrkbe2dfpjy4fekhpdvq
*a*message passing method*for*0-1 integer*linear**programs*. ... Our algorithm is based on*a*decomposition of the original problem into subproblems that are represented as*binary*decision diagrams. ... Implementation*with*BDDs We have described above*a*generic DBCA procedure*for*optimizing*a*Lagrangean*relaxation*of 0-1 integer*linear**programs*and*a*primal search heuristic*for*finding solutions given ...##
###
Image Reconstruction by Multilabel Propagation
[chapter]

2017
*
Lecture Notes in Computer Science
*

The proposed objective function is efficiently minimized via DC

doi:10.1007/978-3-319-58771-4_20
fatcat:inyieqhgxnfqbelqrehezz6x6q
*programming*which amounts to solving*a*sequence of convex*programs*,*with*guaranteed convergence to*a*critical point. ... Each convex*program*is solved by*a*generalized primal dual algorithm. This entails the evaluation of*a*proximal mapping, evaluated efficiently by*a*fixed point iteration. ... We compare our model to state-of-the-art approaches*for*non-*binary*discrete*tomography*in limited angles scenarios. ...##
###
Binary Tomography with Deblurring
[chapter]

2006
*
Lecture Notes in Computer Science
*

We study two scenarios of limited-angle

doi:10.1007/11774938_30
fatcat:n3oxcpnl4zh2hirmxlfjnnmnim
*binary**tomography**with*data distorted*with*an unknown convolution: Either the projection data are taken from*a*blurred object, or the projection data themselves ... To this end,*a*recently introduced Difference-of-Convex-Functions*programming*approach to limited-angle*binary*tomographic reconstruction is complemented*with*Expectation-Maximization iteration. ... Problem Statement*Binary**Tomography*and Reconstruction by DC-*Programming*We consider the reconstruction problem of transmission*tomography**for**binary*objects. ...##
###
CoShaRP: A Convex Program for Single-shot Tomographic Shape Sensing
[article]

2020
*
arXiv
*
pre-print

Hence, the shape

arXiv:2012.04551v2
fatcat:apimporhznfw5atjyziwibw2a4
*prior*transforms*a**linear*ill-posed image estimation problem to*a*non-*linear*problem of estimating the roto-translations of the shapes. ... Moreover, it is more challenging than conventional*tomography*where*a*sufficiently large number of projection angles forms the measurements, allowing*for**a*simple inversion process. ... Acknowledgments The authors thank Nick Luiken*for*stimulating discussions. This work was supported by the Dutch Research Council (grant no. OCENW.XS.039). ...##
###
Non-convex image reconstruction via Expectation Propagation
[article]

2018
*
arXiv
*
pre-print

This maximization can be performed

arXiv:1809.03958v1
fatcat:oyyn5qalyfbh3djw4dtotamocu
*with*standard local optimization tools when the function is concave, but it is generally intractable*for*realistic*priors*, which are non-concave. ... We show, by means of extensive simulations, that, compared to state-of-the-art algorithms*for*this task, Expectation Propagation paired*with*very simple but non log-concave*priors*, is often able to reconstruct ... ), Quadratic*Programming*(QP) (*for*2*smoothness*) and,*for**binary*reconstruction only, the BP algorithm. ...##
###
Limited-view binary tomography reconstruction assisted by shape centroid

2021
*
The Visual Computer
*

In this paper, the

doi:10.1007/s00371-020-02044-8
pmid:33456100
pmcid:PMC7802814
fatcat:7g4qunfwi5di3eks7lxytgjeem
*binary*tomographic reconstruction problem*for*very limited projection data availability is considered. ... Being this inverse problem highly ill-posed, we propose*a*new reconstruction model that uses*a*shape centroid-based regularization term, i.e., we assume that the center of gravity of the object of interest ... This research was supported by the project "Integrated*program**for*training new generation of scientists in the fields of computer science," No. EFOP-3.6.3-VEKOP-16-2017-00002. ...
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