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Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Related publications (37)

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Fringe demodulation using the two-dimensional phase differencing operator

Pramod Rastogi

The Letter proposes a method for phase estimation from a fringe pattern. The proposed method relies on a parametric approach where the phase is locally approximated as a two-dimensional (2D) polynomial, with the ensuing polynomial coefficients as the respe ...

Optical Society of America2012

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Pramod Rastogi, Sai Siva Gorthi

Simultaneous measurement of multidimensional displacements using digital holographic interferometry involves multi-directional illumination of the deformed object and requires the reliable estimation of the resulting multiple interference phase distributio ...

Optical Society of America2012

Phase estimation in digital holographic interferometry using cubic phase function based method

Pramod Rastogi, Sai Siva Gorthi

The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reco ...

Taylor & Francis2010

Analytical Form Of Shepp-Logan Phantom For Parallel Mri

Michaël Unser, Dimitri Nestor Alice Van De Ville, Matthieu Guerquin-Kern

We present an analytical form of ground-truth k-space data for the 2-D Shepp-Logan brain phantom in the presence of multiple and non-homogeneous receiving coils. The analytical form allows us to conduct realistic simulations and validations of reconstructi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Analytical Form of Shepp-Logan Phantom for Parallel MRI

Michaël Unser, Dimitri Nestor Alice Van De Ville, Matthieu Guerquin-Kern

IEEE2010

Vinberg's theta-groups in positive characteristic and Kostant-Weierstrass slices

We generalize the basic results of Vinberg's theta-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We ded ...

Birkhäuser-Verlag, Springer2009

Column Generation for the Split Delivery VRP

Matteo Salani

In this paper we tackle a variation of the Vehicle Routing Problem (VRP) in which each customer can be served by more than one vehicle, each serving a fraction of its demand. This problem is known as the Split Delivery VRP (SDVRP). Due to the potential sav ...

2008

Annihilating polynomials of excellent quadratic forms

If phi is an excellent form, then it is possible to use the dimensions of the higher complements of phi to obtain an annihilating polynomial of phi of low degree. The main result of this paper is the construction of such a polynomial with the help of metho ...

Birkhäuser-Verlag, Springer2008

Invariant generation for P-solvable loops with assignments

Laura Ildiko Kovacs

We discuss interesting properties of a general technique for inferring polynomial invariants for a subfamily of imperative loops, called the P-solvable loops, with assignments only. The approach combines algorithmic combinatorics, polynomial algebra and co ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008

Further Applications of Sector-Based Detection and Short-Term Clustering

Guillaume Lathoud

This paper presents an effective implementation of detection-localization of multiple speech sources with microphone arrays. In particular, the Scaled Conjugate Gradient descent is used for fast and precise localization, within a pre-detected volume of spa ...

IDIAP2006