Concept

Projection (linear algebra)

Related publications (70)

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Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, John Paul Ward, Stamatios Lefkimmiatis

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

Ieee-Inst Electrical Electronics Engineers Inc2013

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Christophe-Aschkan Mery

This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

EPFL2013

Compressed Optical Imaging

Aurélien Bourquard

We address the resolution of inverse problems where visual data must be recovered from incomplete information optically acquired in the spatial domain. The optical acquisition models that are involved share a common mathematical structure consisting of a l ...

EPFL2013

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Revisiting the spread spectrum effect in radio interferometric imaging: a sparse variant of the w-projection algorithm

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

Next-generation radio interferometric telescopes will exhibit non-coplanar baseline configurations and wide field-of-views, inducing a w-modulation of the sky image, which induces the spread spectrum effect. We revisit the impact of this effect on imaging ...

Wiley-Blackwell2013

Analysis of linearization error for goal-oriented adaptivity of nonlinear problems

Luca Dede'

We propose in this talk to address the issue and effect of linearization in the quality of the error estimates in quantities of interest for strongly nonlinear problems. It is well known that the error representation in this case can be decomposed into two ...

International Center for Numerical Methods in Engineering (CIMNE)2013

High-Dimensional Gaussian Process Bandits

Volkan Cevher, Andreas Krause

Many applications in machine learning require optimizing unknown functions defined over a high-dimensional space from noisy samples that are expensive to obtain. We address this notoriously hard challenge, under the assumptions that the function varies onl ...

2013

Global dynamics above the ground state energy for the one-dimensional NLKG equation

Joachim Krieger

In this paperwe obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein–Gordon (NLKG) equation on the line with focusing nonlinearity |u|p−1u, p > 5, provided their energy exceeds that of the ground state o ...

Springer Verlag2012

Shape-Up: Shaping Discrete Geometry with Projections

Mark Pauly, Sofien Bouaziz, Yuliy Gennadievich Schwartzburg, Mario Moacir Deuss

We introduce a uniﬁed optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one-ring cells, volume elements, or featu ...

Wiley-Blackwell2012

Nanoresolution radiology of neurons

Giorgio Margaritondo

We report recent advances in hard-x-ray optics-including record spatial resolution-and in staining techniques that enable synchrotron microradiology to produce neurobiology images of quality comparable to electron and visible microscopy. In addition, micro ...

2012