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Regularized total least squares approach for nonconvolutional linear inverse problems

Wenwu Zhu, Yao Wang, N.P. Galatsanos, Jun Zhang
1999 IEEE Transactions on Image Processing  
In this correspondence, a solution is developed for the regularized total least squares (RTLS) estimate in linear inverse problems where the linear operator is nonconvolutional.  ...  Simulation results show that this method provides more stable and accurate solutions than the regularized least squares and a previously reported total least squares approach, also based on the RQ formulation  ...  SUMMARY AND CONCLUSIONS In this work, A RQF-RTLS approach was proposed for solving the linear inverse problem where the operator is nonconvolutional.  ... 
doi:10.1109/83.799895 pmid:18267442 fatcat:zsgrmfio4fh45hgv5jwwsjzjgu

Subject index

1999 IEEE Transactions on Image Processing  
., + , T-IP Apr 99 564-570 regularized total least squares approach for nonconvolutional lin. inverse problems.  ...  Image resolution Optical tomography regularized total least squares approach for nonconvolutional lin. inverse problems.  ... 
doi:10.1109/tip.1999.806633 fatcat:wl55kzilqzd33dlz6kmq3cljdy

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

M.J. Fadili, E.T. Bullmore
2002 NeuroImage  
Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context  ...  Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error  ...  We also thank two anonymous reviewers for constructive comments on an earlier draft of this paper.  ... 
doi:10.1006/nimg.2001.0955 pmid:11771991 fatcat:t35uetmaejhn3jc64wswbf6pcu

Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems

Patricia K Lamm, Thomas L Scofield
2000 Inverse Problems  
In contrast to classical methods such as Tikhonov regularization, this class of methods preserves the Volterra (causal) structure of the original problem.  ...  This work generalizes earlier results by the first author to the case of a penalized predictor-corrector formulation, functional regularization parameters, and nonconvolution Volterra equations.  ...  Acknowledgments This work was supported in part (for the first author) by the National Science Foundation under contract number NSF DMS 9704899.  ... 
doi:10.1088/0266-5611/16/2/308 fatcat:46xj3tmjgfhppeeibbspr7htqi

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Ed Bullmore, Jalal Fadili, Michael Breakspear, Raymond Salvador, John Suckling, Michael Brammer
2003 Statistical Methods in Medical Research  
We focus on time series resampling by 'wavestrapping' of wavelet coef cients, methods for ef cient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing  ...  Wavelets provide an orthonorma l basis for multiresolution analysis and decorrelation or 'whitening' of nonstationary time series and spatial processes.  ...  (a) WLSˆwavelet-generalized least squares; (b) OLSˆordinary least squares; (c) AR(q)[SBC]â utoregressive least squares using AR models of order q speci ed by minimization of the Schwarz Bayesian criterion  ... 
doi:10.1191/0962280203sm339ra pmid:14599002 fatcat:2xaqqny7vbhkfausalktny3guq

Scalable Surrogate Deconvolution for Identification of Partially-Observable Systems and Brain Modeling [article]

Matthew F Singh, Anxu Wang, Todd S Braver, ShiNung Ching
2020 bioRxiv   pre-print
which generate neuroscientific measurements (e.g. hemodynamics for BOLD fMRI)  ...  These measurements are often generated by approximately linear time-invariant (LTI) dynamical interactions with the hidden system and may therefore be described as a convolution of hidden state-variables  ...  We considered two general approaches to system identification: either using the current gold-standard (joint Kalman estimation) or using surrogate deconvolution for least-squares optimization.  ... 
doi:10.1101/2020.03.20.000661 fatcat:i4mb35raaraotevchq6wlsoxjq

Nonlinear Solution of Linear Inverse Problems by Wavelet–Vaguelette Decomposition

David L. Donoho
1995 Applied and Computational Harmonic Analysis  
We describe the Wavelet-Vaguelette Decomposition (WVD) of a linear inverse problem.  ...  It is a substitute for the singular value decomposition (SVD) of an inverse problem, and it exists for a class of special inverse problems of homogeneous type { such a s n umerical dierentiation, inversion  ...  The windowed SVD method, at least theoretically, includes many other approaches to inversion as special cases, simply by suitable choice of the window function w ; see Bertero (1989) for example.  ... 
doi:10.1006/acha.1995.1008 fatcat:g3xyd23uyzg5jk4oit7v34oxxa

Effect of errors in the system matrix on maximuma posterioriimage reconstruction

Jinyi Qi, Ronald H Huesman
2005 Physics in Medicine and Biology  
Statistically based iterative image reconstruction methods have been developed for emission tomography.  ...  We derived an analytical expression for calculating artifacts in a reconstructed image that are caused by errors in the system matrix using the first-order Taylor series approximation.  ...  However, due to the high computational cost of TLS methods, most of the work has focused on spatially invariant linear inverse problems, although methods have also been proposed for nonconvolutional linear  ... 
doi:10.1088/0031-9155/50/14/007 pmid:16177510 pmcid:PMC1382175 fatcat:4yqowi3rincibmdzhorrjqy5am

Application of general semi-infinite programming to lapidary cutting problems

Anton Winterfeld
2008 European Journal of Operational Research  
The method has been introduced by Stein in [1] , which is also a general reference for this section. 2.1. Lower level problems and Stackelberg games.  ...  An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem.  ...  Mathematically, we model the upcoming inverse problem as a multi-criteria linear programming problem.  ... 
doi:10.1016/j.ejor.2007.01.057 fatcat:6szzfosbgngsbhzmqpc3xac6ry

Mathematics as a Technology–Challenges for the next Ten Years [chapter]

H Neunzert
2005 Lecture Notes in Pure and Applied Mathematics  
Mathematically, we model the upcoming inverse problem as a multi-criteria linear programming problem.  ...  The approximation of spatial derivatives is obtained by the weighted least squares method.  ...  In both cases (direct and inverse problems) we emphasize on the specifi cs related to the non-Newtonian behavior of the polymer. For completeness, we discuss also the Newtonian case.  ... 
doi:10.1201/9781420026511.pt1 fatcat:c6ni6noa3nambgkuftojudjbem

A contribution to (neuromorphic) blind deconvolution by flexible approximated Bayesian estimation

Simone Fiori
2001 Signal Processing  
Bussgang' deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequence de ned on the basis of channel/equalizer cascade model which involves the  ...  In this paper we consider four 'Bussgang' blind deconvolution algorithms for uniformly-distributed source signals and investigate their numerical performances as well as some their analytical features.  ...  , but after approaching the optimum inverse lter it diverges.  ... 
doi:10.1016/s0165-1684(01)00108-6 fatcat:2dsed4jmujhgnpgtdmqgawfbs4

Diffraction by image processing and its application in materials science

Joachim Ohser, Katja Schladitz, Karsten Koch, Michael Nöthe
2005 Zeitschrift für Metallkunde  
More general approaches can be found in [6, Chapter 11] and [23].  ...  See [1, 2] for the theoretic foundations for one and two dimensional point patterns and [22] and [17] for applications to ecological data.  ...  The authors are grateful to the Deutsche Forschungsgemeinschaft (Oh 59/5-1) for financial support. We are indepted to T. Sych for producing the visualizations of the sinter material.  ... 
doi:10.3139/146.101094 fatcat:zjvl7coqqrfatgaxw65twc4vh4

Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

Ganchi Zhang, Nick Kingsbury
2015 Digital signal processing (Print)  
The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive  ...  Compared with MAP, VB inference can be seen as a more principled approach, which should find improved solutions to inverse problems.  ...  Wavelet-based regularization methods are good for image restoration problems because wavelet coefficients tend to be sparse for most image types.  ... 
doi:10.1016/j.dsp.2015.04.011 fatcat:zxfslb4hmren7ffggich5gc4xi

On sparse connectivity, adversarial robustness, and a novel model of the artificial neuron [article]

Sergey Bochkanov
2020 arXiv   pre-print
We demonstrate the feasibility of our approach through experiments on SVHN and GTSRB benchmarks.  ...  It is interesting that these advances were made using two ideas that are decades old: (a) an artificial neuron based on a linear summator and (b) SGD training.  ...  Now, instead of a nonconvex, nonsmooth, nonlinear least squares problem we have a combinatorial optimization problem: min w0,w1,w2 i min max j (w 0,j ·X i,j ) , max j (w 1,j ·X i,j ) , max j (w 2,j ·X  ... 
arXiv:2006.09510v1 fatcat:rfgkqyyvavb2xattqgp2sbdryu

A new algorithm for topology optimization using a level-set method

Samuel Amstutz, Heiko Andrä
2006 Journal of Computational Physics  
This results in a new algorithm allowing for all kinds of topology changes.  ...  algorithms use a Hamilton-Jacobi equation to connect the evolution of the level-set function with the deformation of the contours, and consequently they cannot create any new holes in the domain (at least  ...  The authors are grateful to Oleg Iliev for his valuable help concerning Section 5.  ... 
doi:10.1016/j.jcp.2005.12.015 fatcat:2ip4frr5sjh6dlfq5zqy5odopi
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