1.3k citations · 1.5k across the 23 of their papers we have counts for
29 papers
Matrix Discrepancy for Representations of Finite Groups
Afonso S. Bandeira, Helmut Bölcskei
We prove the group version of the Matrix Spencer conjecture. For every finite group , there exist signs such that $$\left\| \sum_{g\in G} \varepsilon_…
Entropy and Minimax Risk of Hypoelliptic Pseudodifferential Operators
Thomas Allard, Helmut Bölcskei
We characterize the entropy and minimax risk of a broad class of compact pseudodifferential operators. Under suitable decay and regularity conditions on the symbol, we combine a We…
Metric Entropy of Ellipsoids in Banach Spaces: Techniques and Precise Asymptotics
Thomas Allard, Helmut Bölcskei
We develop new techniques for computing the metric entropy of ellipsoids -- with polynomially decaying semi-axes -- in Banach spaces. Besides leading to a unified and comprehensive…
Metric-Entropy Limits on the Approximation of Nonlinear Dynamical Systems
Yang Pan, Clemens Hutter, Helmut Bölcskei
This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate non…
Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces
Thomas Allard, Helmut Bölcskei
We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be app…
Metric Entropy of Analytic Function Classes via Ellipsoidal Methods
Thomas Allard, Helmut Bölcskei
We present a systematic methodology for characterizing the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. The approach does not rely on th…
Affine symmetries and neural network identifiability
Verner Vlačić, Helmut Bölcskei
We address the following question of neural network identifiability: Suppose we are given a function and a nonlinearity . Can we specify the arch…
Necessary Conditions for K/2 Degrees of Freedom
Recep Gül, Helmut Bölcskei, Shlomo Shamai
Stotz et al., 2016, reported a sufficient (injectivity) condition for each user in a K-user single-antenna constant interference channel to achieve 1/2 degree of freedom. The prese…
Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation
Winfried Auzinger, Thomas Kassebacher, Othmar Koch +1
Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schrödinger equations. In particular, the Schrödinger-Poiss…
Deep Convolutional Neural Networks Based on Semi-Discrete Frames
Thomas Wiatowski, Helmut Bölcskei
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Malla…
Density Criteria for the Identification of Linear Time-Varying Systems
Céline Aubel, Helmut Bölcskei
This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that s…
Information-Theoretic Limits of Matrix Completion
Erwin Riegler, David Stotz, Helmut Bölcskei
We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity".…
Explicit and almost sure conditions for K/2 degrees of freedom
David Stotz, Helmut Bölcskei
It is well known that in K-user constant single-antenna interference channels K/2 degrees of freedom (DoF) can be achieved for almost all channel matrices. Explicit conditions on t…
Almost Lossless Analog Signal Separation
David Stotz, Erwin Riegler, Helmut Bölcskei
We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals from a noiseless sum of linear me…
Degrees of freedom in vector interference channels
David Stotz, Helmut Bölcskei
This paper continues the Wu-Shamai-Verdu program [3] on characterizing the degrees of freedom (DoF) of interference channels (ICs) through Renyi information dimension. Specifically…
Sparse Signal Recovery in Hilbert Spaces
Graeme Pope, Helmut Bölcskei
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general…
Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka's Theorem
Veniamin I. Morgenshtern, Erwin Riegler, Wei Yang +4
We find the capacity pre-log of a temporally correlated Rayleigh block-fading SIMO channel in the noncoherent setting. It is well known that for block-length L and rank of the chan…
On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity
Giuseppe Durisi, Veniamin I. Morgenshtern, Helmut Bölcskei
The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the s…
Noncoherent SIMO Pre-Log via Resolution of Singularities
Erwin Riegler, Veniamin I. Morgenshtern, Giuseppe Durisi +3
We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Our result holds for ar…
Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets
Patrick Kuppinger, Giuseppe Durisi, Helmut Bölcskei
We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. This uncertainty relation is relevant…
Recovery of Sparsely Corrupted Signals
Christoph Studer, Patrick Kuppinger, Graeme Pope +1
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admi…
Where is Randomness Needed to Break the Square-Root Bottleneck?
Patrick Kuppinger, Giuseppe Durisi, Helmut Bölcskei
As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all th…
The SIMO Pre-Log Can Be Larger Than the SISO Pre-Log
Veniamin I. Morgenshtern, Giuseppe Durisi, Helmut Bölcskei
We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Surprisingly, when the…
Improved Sparsity Thresholds Through Dictionary Splitting
Patrick Kuppinger, Giuseppe Durisi, Helmut Bölcskei
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. Whil…