On Sampling Lattices with Similarity Scaling Relationships

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The technological advancements of the past decades have allowed transforming an increasing part of our daily actions and decisions into storable data, leading to a radical change in the scale and scope of available data in relation to virtually any object ...

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded r ...

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...

The invention relates to a method and an apparatus for encoding and/or decoding digital images, wherein said encoding apparatus (1100) comprises processing means (1110) configured for determining weights of a graph related to an image by minimizing a cost ...

Recent works have shown that the state-feedback decoupling of capacitor voltage allows for drastic bandwidth enlarging of current controllers for grid-forming converters in islanded microgrids. Furthermore, Smith predictor and lead compensation have been a ...

We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinog ...

In this paper we present FRIDA—an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state- of-the-art resolution at extremely low signal-to-noise ratios. It work ...

It is a classic problem to estimate continuous-time sparse signals, like point sources in a direction-of-arrival problem, or pulses in a time-of-flight measurement. The earliest occurrence is the estimation of sinusoids in time series using Prony's method. ...

Generalized linear models, where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x, arise in a range of applications in nonlinear filtering and regression. Approximate message passing (AMP) methods, b ...

The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based on Gaussian appr ...

The notion of non-invasive, high-resolution spatial mapping of metabolite concentrations has long enticed the medical community. While magnetic resonance spectroscopic imaging (MRSI) is capable of achieving the requisite spatio-spectral localization, it ha ...

The general integral expressions for the elements of the ground impedance matrix do not have an analytical inverse transform in the time domain. Therefore, the ground transient resistance of a multiconductor line is commonly evaluated in the time domain by ...

A stable method for the analysis of lossy transmission lines with nonlinear loads is presented. The simulation employs the time marching (TM) method for solving the convolution equations in the time domain. To cope with the late-time instability of the TM ...

A method and device for reducing the computational complexity of a processing algorithm, of a discrete signal, in particular of the spectral estimation and analysis of bio-signals, with minimum or no quality loss, which comprises steps of (a) choosing a do ...

Generalized Linear Models (GLMs), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x arise in a range of applications in nonlinear filtering and regression. Approximate Message Passing (AMP) meth ...

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform indepe ...

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

On Sampling Lattices with Similarity Scaling Relationships

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Discrete choice modeling in the era of big data

Fourier non-uniqueness sets from totally real number fields

Fourier Sampling in Signal Processing and Numerical Linear Algebra

A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Methods and apparatuses for encoding and decoding digital images or video streams

Full Discrete Modeling, Controller Design, and Sensitivity Analysis for High-Performance Grid-Forming Converters in Islanded Microgrids

On Short Sums Of Trace Functions

FRIDA: FRI-Based DOA Estimation For Arbitrary Array Layouts

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Fixed Points of Generalized Approximate Message Passing with Arbitrary Matrices

Magnetic resonance spectroscopic imaging at superresolution: Overview and perspectives

An Improved Approach for the Calculation of the Transient Ground Resistance Matrix of Multiconductor Lines

Stable Simulation of Nonlinearly Loaded Lossy Transmission Lines with Time Marching Approach

Method and apparatus for low complexity spectral analysis of bio-signals

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Optimized Kaiser-Bessel Window Functions for Computed Tomography

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms