181 citations · 702 across the 49 of their papers we have counts for
18 papers · 1 filter
Information-Theoretic Foundations of DNA Data Storage
Ilan Shomorony, Reinhard Heckel
Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Thanks to rapid technological advances, DNA storage is becoming practi…
Achieving the Capacity of a DNA Storage Channel with Linear Coding Schemes
Kel Levick, Reinhard Heckel, Ilan Shomorony
Due to the redundant nature of DNA synthesis and sequencing technologies, a basic model for a DNA storage system is a multi-draw "shuffling-sampling" channel. In this model, a rand…
DNA-Based Storage: Models and Fundamental Limits
Ilan Shomorony, Reinhard Heckel
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and trade-offs of DNA-based s…
Capacity Results for the Noisy Shuffling Channel
Ilan Shomorony, Reinhard Heckel
Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel,…
Super-resolution radar imaging via convex optimization
Reinhard Heckel
A radar system emits probing signals and records the reflections. Estimating the relative angles, delays, and Doppler shifts from the received signals allows to determine the locat…
Rate-Optimal Denoising with Deep Neural Networks
Reinhard Heckel, Wen Huang, Paul Hand +1
Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying princip…
Fundamental Limits of DNA Storage Systems
Reinhard Heckel, Ilan Shomorony, Kannan Ramchandran +1
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based st…
Generalized Line Spectral Estimation via Convex Optimization
Reinhard Heckel, Mahdi Soltanolkotabi
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal proces…
Super-Resolution MIMO Radar
Reinhard Heckel
A multiple input, multiple output (MIMO) radar emits probings signals with multiple transmit antennas and records the reflections from targets with multiple receive antennas. Estim…
Super-Resolution Radar
Reinhard Heckel, Veniamin I. Morgenshtern, Mahdi Soltanolkotabi
In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the in…
Subspace clustering of dimensionality-reduced data
Reinhard Heckel, Michael Tschannen, Helmut Bölcskei
Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one ma…
Noisy Subspace Clustering via Thresholding
Reinhard Heckel, Helmut Bölcskei
We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions,…
Subspace Clustering via Thresholding and Spectral Clustering
Reinhard Heckel, Helmut Bölcskei
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orie…
Joint Sparsity with Different Measurement Matrices
Reinhard Heckel, Helmut Bölcskei
We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises natural…
Bounds on the Average Sensitivity of Nested Canalizing Functions
Johannes Georg Klotz, Reinhard Heckel, Steffen Schober
Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It ha…
Identification of Sparse Linear Operators
Reinhard Heckel, Helmut Bölcskei
We consider the problem of identifying a linear deterministic operator from its response to a given probing signal. For a large class of linear operators, we show that stable ident…
Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations
Reinhard Heckel, Steffen Schober, Martin Bossert
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determ…
Compressive Identification of Linear Operators
Reinhard Heckel, Helmut Bölcskei
We consider the problem of identifying a linear deterministic operator from an input-output measurement. For the large class of continuous (and hence bounded) operators, under addi…