@book {Simula.SC.592,
	title = {Scale Space and Variational Methods in Computer Vision},
	volume = {5567},
	year = {2009},
	publisher = {Springer},
	abstract = {Lecture Notes in Computer Science, Second International Conference, Voss, Norway, June 2009},
	isbn = {ISBN 978-3-642-02255-5},
	author = {Tai, Xue-Cheng and M{\o}rken, Knut and Ola Marius {Lysaker} and Lie, Knut-Andreas}
}
@article {Simula.SC.148,
	title = {Level Set Method for Positron Emission Tomography},
	journal = {International Journal of Biomedical Imaging},
	number = {2007},
	year = {2007},
	pages = {1-15},
	abstract = {In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a level set approach. The level set method is used to capture the coarse scale information and the discontinuities of the concentration coefficients. An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way. We utilize a multiple level set formulation to represent the geometry of the objects in the scene. The proposed algorithm can be applied to any PET configuration, without major modifications.},
	author = {Chan, Tony and Li, Hongwei and Ola Marius {Lysaker} and Tai, Xue-Cheng}
}
@article {Lie.2006.1,
	title = {A Binary Level Set Model and Some Applications to Mumford-Shah Image Segmentation},
	journal = {IEEE Transactions on Image Processing},
	volume = {15},
	number = {5},
	year = {2006},
	month = {May},
	pages = {1171-1181},
	abstract = {In this work we propose a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e. it can only be 1 or -1, and is thus related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new level set method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.},
	author = {Lie, Johan and Ola Marius {Lysaker} and Tai, Xue-Cheng}
}
@article {Lysaker.2006.2,
	title = {Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional},
	journal = {International Journal of Computer Vision},
	volume = {66},
	number = {1},
	year = {2006},
	month = {January},
	pages = {5-18},
	abstract = {A noise removal technique using partial differential equations (PDEs) is proposed here. It combines the Total Variational (TV) filter with a fourth-order PDE filter. The combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions. A weighting function is used in an iterative way to combine the solutions of the TV-filter and the fourth-order filter. Numerical experiments confirm that the new method is able to use less restrictive time step than the fourth-order filter. Numerical examples using images with objects consisting of edge, flat and intermediate regions illustrate advantages of the proposed model.},
	author = {Ola Marius {Lysaker} and Tai, Xue-Cheng}
}
@article {Lie.2006.2,
	title = {A Variant of the Level Set Method and Applications to Image Segmentation},
	journal = {Mathematics of Computation},
	volume = {75},
	number = {255},
	year = {2006},
	note = {Article electronically published on February 22, 2006},
	month = {July 2006},
	pages = {1155-1174},
	abstract = {In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functions are utilized to identify up to 2^n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If 2^n phases should be identified, the level set function must approach 2^n predetermined constants. We just need one level set function to represent 2^n unique phases and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the non-differentiability of the Delta and Heaviside functions. Numerical examples are given and we also compare our method with related approaches.},
	author = {Lie, Johan and Ola Marius {Lysaker} and Tai, Xue-Cheng}
}
@article {Lie.2005.2,
	title = {A Piecewise Constant Level Set Framework},
	journal = {International Journal of Numerical Analysis and Modeling},
	volume = {2},
	number = {4},
	year = {2005},
	pages = {422-438},
	abstract = {In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface problems, we minimize a smooth locally convex functional under a constraint. We show numerical results using the methods for image segmentation.},
	author = {Lie, Johan and Ola Marius {Lysaker} and Tai, Xue-Cheng}
}
@article {SC.4.Lysaker.2004,
	title = {Noise Removal Using Smoothed Normals and Surface Fitting},
	journal = {IEEE Transactions on Image Processing},
	volume = {13},
	number = {10},
	year = {2004},
	pages = {1345-1357},
	abstract = {In this work, we use partial differential equation techniques to remove noise from digital images. The removal is done in two steps. We first use a total-variation filter to smooth the normal vectors of the level curves of a noise image. After this, we try to find a surface to fit the smoothed normal vectors. For each of these two stages, the problem is reduced to a nonlinear partial differential equation. Finite difference schemes are used to solve these equations. A broad range of numerical examples are given in the paper.},
	author = {Ola Marius {Lysaker} and Osher, S. and Tai, Xue-Cheng}
}
@inbook {SC.5.Heimsund.2003,
	title = {Level Set Methods for a Parameter Identification Problem},
	booktitle = {Analysis and optimization of differential systems},
	year = {2003},
	pages = {189-200},
	publisher = {Kluwer Academic Publishers},
	organization = {Kluwer Academic Publishers},
	author = {B. O. {Heimsund} and T. F. {Chan} and Nilssen, Trygve Kastberg and Tai, Xue-Cheng},
	editor = {Barbu, V. and Lasiecka, I. and Tiba, D. and Varsan, C.}
}
@article {SC.4.Lysaker.2003,
	title = {Noise Removal Using Fourth-Order Partial Differential Equation With Applications to Medical Magnetic Resonance Images in Space and Time},
	journal = {IEEE Transactions on Image Processing},
	volume = {12},
	number = {12},
	year = {2003},
	pages = {1579-1590},
	abstract = {We introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magnetic resonance images, both in space and time, as well as on nonmedical synthesized test images. Our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail, even at poor signal-to-noise ratio. We have also compared our method with related PDE models.},
	author = {Ola Marius {Lysaker} and Lundervold, Arvid and Tai, Xue-Cheng}
}
@article {SC.4.Nilssen.2003,
	title = {Permeability Estimation With the Augmented Lagrangian Method for a Nonlinear Diffusion Equation},
	journal = {Computational Geosciences},
	volume = {7},
	year = {2003},
	pages = {27-47},
	author = {Nilssen, Trygve Kastberg and Mannseth, T. and Tai, Xue-Cheng}
}
@article {SC.4.Mardal.2002,
	title = {A Robust Finite Element Method for Darcy-Stokes Flow},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {40},
	year = {2002},
	pages = {1605-1631},
	author = {Mardal, Kent-Andre and Tai, Xue-Cheng and Winther, Ragnar}
}
@inproceedings {Lysaker.2001.1,
	title = {Noise Removal With Tissue Boundary Preservation Using Fourth-Order Partial Differential Equations},
	journal = {Proc. Intl. Soc. Mag. Reson. Med 9, 2001},
	year = {2001},
	publisher = {International Society for Magnetic Resonance in Medicine, ISMRM-ESMRMB},
	type = {1},
	author = {Ola Marius {Lysaker} and Lundervold, Arvid and Tai, Xue-Cheng and Bock, Michael and Schad, Lothar}
}
@misc {SC.8.Nilssen.2001,
	title = {Permeability Estimation With the Augmented Lagrangian Method for Nonlinear Diffusion Equations},
	howpublished = {Talk at the International Parallel CFD 2001 Conference, Egmond aan Zee, The Netherlands},
	year = {2001},
	author = {Nilssen, Trygve Kastberg and Mannseth, T. and Tai, Xue-Cheng}
}
@article {SC.4.Nilssen.2001,
	title = {A Robust Nonconforming H2-Element},
	journal = {Mathematics of Computation},
	volume = {70},
	year = {2001},
	pages = {489-505},
	author = {Nilssen, Trygve Kastberg and Tai, Xue-Cheng and Winther, Ragnar}
}
