Publications related to Quasi-Interpolating Spline Models for Hexagonally-Sampled Data

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Rethinking Sampling in Parallel MRI: A Data-Driven Approach

Volkan Cevher, Baran Gözcü, Thomas Sanchez

In the last decade, Compressive Sensing (CS) has emerged as the most promising, model-driven approach to accelerate MRI scans. CS relies on the key sparsity assumption and proposes random sampling for data acquisition. The practical CS approaches in MRI em ...

IEEE2019

A note on discrete lattice-periodic sets with an application to Archimedean tilings

Matthias Schymura

Cao and Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that the vertex set of every Archimedean tiling is the union of translates of a fixed lattice, we take a more general v ...

SPRINGER HEIDELBERG2019

The AKLT Model on a Hexagonal Chain is Gapped

Marius Christopher Lemm

In 1987, Affleck, Kennedy, Lieb, and Tasaki introduced the AKLT spin chain and proved that it has a spectral gap above the ground state. Their concurrent conjecture that the two-dimensional AKLT model on the hexagonal lattice is also gapped remains open. I ...

2019

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

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

Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Adrien Georges Jean Besson, Olivier Bernard

The theory of compressed sensing (CS) leverages upon structure of signals in order to reduce the number of samples needed to reconstruct a signal, compared to the Nyquist rate. Although CS approaches have been proposed for ultrasound (US) imaging with prom ...

Ieee2016

An Algorithm to Compensate the Effects of Spurious PLL Tones in Spectrum Sensing Architectures

Ali H. Sayed

In a nonideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used as a sampling clock to an analog-to-digital converter (ADC), it creates spurious sidebands in the sampled data a ...

IEEE2012

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

Michaël Unser, John Paul Ward, Hagay Kirshner

We consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternativ ...

IEEE2012

Resolution-Invariant Separable Arma Modeling Of Images

Michaël Unser, Aurélien Bourquard, Hagay Kirshner

We suggest a continuous-domain stochastic modeling of images that is invariant to spatial resolution. Specifically, we are proposing an estimator that is calibrated with respect to the sampling step, and that can potentially handle aliased data. Motivated ...

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Quasi-Interpolating Spline Models for Hexagonally-Sampled Data

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Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Rethinking Sampling in Parallel MRI: A Data-Driven Approach

A note on discrete lattice-periodic sets with an application to Archimedean tilings

The AKLT Model on a Hexagonal Chain is Gapped

Shapes from Pixels

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

An Algorithm to Compensate the Effects of Spurious PLL Tones in Spectrum Sensing Architectures

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

Resolution-Invariant Separable Arma Modeling Of Images

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Shapes from Pixels

Rethinking Sampling in Parallel MRI: A Data-Driven Approach

Resolution-Invariant Separable Arma Modeling Of Images

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

A note on discrete lattice-periodic sets with an application to Archimedean tilings

The AKLT Model on a Hexagonal Chain is Gapped

Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

An Algorithm to Compensate the Effects of Spurious PLL Tones in Spectrum Sensing Architectures