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An Entropic Perturbation Approach to TV-Minimization for Limited-Data Tomography [chapter]

Andreea Deniţiu, Stefania Petra, Claudius Schnörr, Christoph Schnörr
2014 Lecture Notes in Computer Science  
We propose an entropic perturbation of the objective that enables to apply efficient methodologies from unconstrained optimization to the perturbed dual program.  ...  As a consequence, the large-scale optimization task based on total-variation minimization subject to tomographic projection constraints is considerably more complex than basic 1-programming for sparse  ...  We work out a corresponding approach to our specific reconstruction problem min u TV(u) subject to Au = b , (1) that minimizes the total variation TV(u) subject to the projection constraints.  ... 
doi:10.1007/978-3-319-09955-2_22 fatcat:wh466yj3fjhojlnvhcxkdimnoy

Information theoretic regularization in diffuse optical tomography

Christos Panagiotou, Sangeetha Somayajula, Adam P. Gibson, Martin Schweiger, Richard M. Leahy, Simon R. Arridge
2009 Optical Society of America. Journal A: Optics, Image Science, and Vision  
However, limited information regarding the probed anatomy is known prior to the reconstruction process.  ...  We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results obtained by numerical simulations as well as experimental data.  ...  Diffusion optical tomography using entropic priors.  ... 
doi:10.1364/josaa.26.001277 pmid:19412248 fatcat:m66nq2adhzdnvb6nqcvgwf73p4

Compressively Characterizing High-Dimensional Entangled States with Complementary, Random Filtering

Gregory A. Howland, Samuel H. Knarr, James Schneeloch, Daniel J. Lum, John C. Howell
2016 Physical Review X  
Finally, we use entropic inequalities to witness entanglement without a density matrix.  ...  Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements.  ...  Witnessing entanglement To witness and quantify entanglement, we violate an entropic steering inequality [51] [52] [53] (see Ref.  ... 
doi:10.1103/physrevx.6.021018 fatcat:pjdc53qjkjdctpmulh2vphwsu4

Learning to solve inverse problems using Wasserstein loss [article]

Jonas Adler, Axel Ringh, Ozan Öktem, Johan Karlsson
2017 arXiv   pre-print
Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.  ...  This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality.  ...  One approach for addressing this problem was proposed by Cuturi [10] that introduces an entropic regularizing term D(M ) = n i,j=1 (m ij log(m ij ) − m ij + 1) for approximating the transference plan  ... 
arXiv:1710.10898v1 fatcat:zykmduxa6vh6fpra4dxo6wa2xa

Data-Driven Mirror Descent with Input-Convex Neural Networks [article]

Hong Ye Tan, Subhadip Mukherjee, Junqi Tang, Carola-Bibiane Schönlieb
2022 arXiv   pre-print
Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data.  ...  We derive convergence rate bounds for the proposed learned mirror descent (LMD) approach with an approximate inverse mirror map and perform extensive numerical evaluation on various convex problems such  ...  robust convergence for tomography problems [29] .  ... 
arXiv:2206.06733v2 fatcat:n3tubmufurbxjmjz7md3svtotq

Indirect Image Registration with Large Diffeomorphic Deformations

Chong Chen, Ozan Öktem
2018 SIAM Journal of Imaging Sciences  
The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.  ...  The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect  ...  The authors would like to thank Barbara Gris and Oliver Verdier for valuable comments and remarks.  ... 
doi:10.1137/17m1134627 fatcat:pncuaoa4jnelrcczeuwzgymxvy

Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing [article]

Vishal Monga, Yuelong Li, Yonina C. Eldar
2020 arXiv   pre-print
Unrolling methods were first proposed to develop fast neural network approximations for sparse coding.  ...  Finally, we provide a discussion on current limitations of unrolling and suggest possible future research directions.  ...  From an impact standpoint, this line of research may provide newer additions to approaches for semi-supervised/unsupervised learning, and offer practical benefits when training data is limited or when  ... 
arXiv:1912.10557v3 fatcat:klkwcacburca3hr63m7v77pvnq

Variational Methods for Discrete Tomography [article]

Andreea-Marieta Denitiu
Moreover, a closer look is given to handling large data volumes, by adding different perturbations (entropic, quadratic) to the already constrained linear program.  ...  In empirical assessments, perturbation has lead to an increased reconstruction rate.  ...  Experimental finite perturbation property of the entropic approach.  ... 
doi:10.11588/heidok.00021683 fatcat:vefxewd7afhgblvqy6ljillfqa

Quantum Probability Estimation for Randomness with Quantum Side Information [article]

Emanuel Knill, Yanbao Zhang, Honghao Fu
2020 arXiv   pre-print
For the class of (k,2,2) Bell-test configurations we provide schemas for directly optimizing QEFs to overcome the limitations of entropy-estimator-based constructions.  ...  We obtain and apply QEFs for examples involving the (2,2,2) Bell-test configuration to demonstrate substantial improvements in finite-data efficiency.  ...  This work includes contributions of the National Institute of Standards and Technology, which are not subject to U.S. copyright.  ... 
arXiv:1806.04553v3 fatcat:i5lpgdfqgbc2poaycx4cahtjli

Field-cycling NMR relaxometry

Rainer Kimmich, Esteban Anoardo
2004 Progress in nuclear magnetic resonance spectroscopy  
The melt data for M w . M c < 24; 000 refer to the molecular-weight independent chain-mode regimes I (high-mode number limit) and II (low-mode number limit).  ...  The data refer to the molecular-weight independent chain-mode regimes I (high-mode number limit) and II (low-mode number limit) [138] .  ...  time constants consequently is t d =t b < 230: An Arrhenius law is assumed in order to accunt for the temperature dependence:  ... 
doi:10.1016/j.pnmrs.2004.03.002 fatcat:p2nze734dzbmtekqsvevdpfvcy

Field-Cycling NMR Relaxometry [chapter]

Rainer Kimmich
1997 NMR  
The melt data for M w . M c < 24; 000 refer to the molecular-weight independent chain-mode regimes I (high-mode number limit) and II (low-mode number limit).  ...  The data refer to the molecular-weight independent chain-mode regimes I (high-mode number limit) and II (low-mode number limit) [138] .  ...  time constants consequently is t d =t b < 230: An Arrhenius law is assumed in order to accunt for the temperature dependence:  ... 
doi:10.1007/978-3-642-60582-6_15 fatcat:itfjgqyy4fbjdkhspceybsz5nm

Psycho-computational modelling of the mental lexicon [chapter]

Vito Pirrelli, Claudia Marzi, Marcello Ferro, Franco Alberto Cardillo, Harald R. Baayen, Petar Milin
2020 Word Knowledge and Word Usage  
, and for making it possible to publish the present editorial effort as an open access volume with generous funding of the NetWordS project in the years 2011-2015.  ...  We express our hope that similar programmes will continue to be launched and funded in Europe in the years to come.  ...  Although the Stochastic OT approach accounts well for the data, there are several reasons not to favor this approach.  ... 
doi:10.1515/9783110440577-002 fatcat:3gntrjuqefg3fk64dvgw253p2i

Quantum Mind 2003, Consciousness, Quantum Physics and the Brain. March 15-19, 2003, The University of Arizona, Tucson, Arizona

Editorial NQ
2007 NeuroQuantology  
Critics deride this comparison as a mere "minimization of mysteries" and quickly point out that the brain is too warm for quantum computation which in the technological realm requires extreme cold to avoid  ...  However quantum computation would surely be advantageous from an evolutionary perspective, and biology has had 4 billion years to solve the decoherence problem and evolve quantum mechanisms.  ...  The image formation processing is an integral part of the sensor; without it there is nothing to see. The same can be said for many other computerdependent sensors such as computer-aided tomography.  ... 
doi:10.14704/nq.2003.1.3.23 fatcat:e76cv2ivqjdbxolv2hbls67gqu

Deformation and transport of image data [article]

Sebastian Jonas Neumayer, Technische Universität Berlin, Gabriele Steidl
For both models, existence of minimizers is shown under the assumption that the data lies in a finite-dimensional Hadamard manifold.  ...  These modifications enable us to obtain promising reconstructions for computed tomography with a very sparse number of angles.  ...  This is, for instance, the case in limited-angle computed tomography [116, 208] , where limited-angle data is acquired in order to minimize exposure time of organisms to X-radiation.  ... 
doi:10.14279/depositonce-11298 fatcat:43defnxqrbga5pd46vmancbflu

Quantitative Susceptibility Mapping in the Human Brain

Diana Khabipova
Also you introduced me to the delicious Belgian Beer for drinks in the Satelite and snowshoeing in Les Diablerets.  ...  David Norris I would like to thank for giving me the opportunity to be a researcher in your MR group in the Donders Institutes during my SNF Doc.Mobility year.  ...  (a), ε for l 1 TV norm (b) minimization with binary prior and λ for modulated closed form solution (c).  ... 
doi:10.5075/epfl-thesis-7050 fatcat:essfz3dvlnd33klaulagsa5cka
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