26 citations · 123 across the 11 of their papers we have counts for
15 papers
How well do fast discrete trigonometric transforms work for parametric numerical integration?
Gerlind Plonka, Daniel Potts, Manfred Tasche
The fast Fourier transform (FFT) and its real counterparts, the fast algorithms of the discrete cosine transform (DCT) and the discrete sine transform (DST), are frequently employe…
MOCCA: A Fast Algorithm for Parallel MRI Reconstruction Using Model Based Coil Calibration
Gerlind Plonka, Yannick Riebe
We propose a new fast algorithm for simultaneous recovery of the coil sensitivities and of the magnetization image from incomplete Fourier measurements in parallel MRI. Our approac…
Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models
Gerlind Plonka, Yannick Riebe, Yurii Kolomoitsev
We analyze the structure of a one-dimensional deep ReLU neural network (ReLU DNN) in comparison to the model of continuous piecewise linear (CPL) spline functions with arbitrary kn…
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
Nadiia Derevianko, Gerlind Plonka, Markus Petz
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm f…
Frame Soft Shrinkage as Proximity Operator
Marzieh Hassanasab, Sebastian Neumayer, Gerlind Plonka +3
Let and be real Hilbert spaces and an injective operator with closed range and Moore-Penrose inverse $T^\dagge…
Frame Soft Shrinkage Operators are Proximity Operators
Jakob Alexander Geppert, Gerlind Plonka
In this paper, we show that the commonly used frame soft shrinkage operator, that maps a given vector onto the vector ${\mathbf T}^{\dagger} S_γ {…
The Generalized Operator Based Prony Method
Kilian Stampfer, Gerlind Plonka
The generalized Prony method introduced by Peter & Plonka (2013) is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansi…
Real Sparse Fast DCT for Vectors with Short Support
Sina Bittens, Gerlind Plonka
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector ,…
Sparse Fast DCT for Vectors with One-block Support
Sina Bittens, Gerlind Plonka
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II that reconstructs the input vector $\mathbf{x}\in\mathbb{R}^{N}…
Sparse phase retrieval of one-dimensional signals by Prony's method
Robert Beinert, Gerlind Plonka
In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B…
Application of the AAK theory for sparse approximation of exponential sums
Gerlind Plonka, Vlada Pototskaia
In this paper, we derive a new method for optimal - and -approximation of discrete signals on whose entries can be represented as an exponential…
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
Robert Beinert, Gerlind Plonka
Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information a…
A sparse Fast Fourier Algorithm for Real Nonnegative Vectors
Gerlind Plonka, Katrin Wannenwetsch
In this paper we propose a new fast Fourier transform to recover a real nonnegative signal from its discrete Fourier transform. If the signal appears to hav…
Pseudo-inverses of difference matrices and their application to sparse signal approximation
Gerlind Plonka, Sebastian Hoffmann, Joachim Weickert
We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization app…
A deterministic sparse FFT algorithm for vectors with small support
Gerlind Plonka, Katrin Wannenwetsch
In this paper we consider the special case where a discrete signal of length N is known to vanish outside a support interval of length . If the support length …