Publications related to Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Learning-based subsampling

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic, Yen-Huan Li, Luca Baldassarre, Baran Gözcü

The present invention concerns a method of sampling a test signal. The method comprises: acquiring (21) training signals sampled at a plurality of sampling locations; running (23) an optimization procedure for determining an index set of n indices, represe ...

2017

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

Shapes from Pixels

Mitra Fatemi

In today's digital world, sampling is at the heart of any signal acquisition device. Imaging devices are ubiquitous examples that capture two-dimensional visual signals and store them as the pixels of discrete images. The main concern is whether and how th ...

EPFL2016

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Matthieu Martin Jean-André Simeoni

Estimating intensity fields of stochastic phenomenons is of crucial interest in many scientific applications. Typical experimental setups involve an acquisition system, that subsequently filters and samples the probed intensity field. This equivalently def ...

2016

Influence of loading history on mechanical properties of biomaterials

Tom Charles Maurice Walet

It is known that the mechanical response to load or displacement of a biological tissue can highly vary from one cycle to the next. Therefore, in order to establish a reference state for repeating data measurements, tissues are subjected to a preliminary s ...

2016

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

Serge Vaudenay, Pouyan Sepehrdad, Petr Susil

The best way of selecting samples in algebraic attacks against block ciphers is not well explored and understood. We introduce a simple strategy for selecting the plaintexts and demonstrate its strength by breaking reduced-round KATAN, LBLOCK and SIMON. Fo ...

Springer Verlag2016

BDD Minimization for Approximate Computing

Mathias Soeken, Arun Chandrasekharan

We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representa ...

IEEE2016

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

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Learning-based subsampling

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Shapes from Pixels

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Influence of loading history on mechanical properties of biomaterials

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

BDD Minimization for Approximate Computing

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Learning-based subsampling

Sampling and Reconstruction of Shapes with Algebraic Boundaries

BDD Minimization for Approximate Computing

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Shapes from Pixels

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Influence of loading history on mechanical properties of biomaterials