167 citations · 800 across the 50 of their papers we have counts for
34 papers · 1 filter
Fast One-Pass Sparse Approximation of the Top Eigenvectors of Huge Approximately Low-Rank Matrices? Yes, !
Edem Boahen, Simone Brugiapaglia, Hung-Hsu Chou +2
Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massi…
On the reconstruction of bandlimited signals from random samples quantized via noise-shaping
Rohan Joy, Felix Krahmer, Alessandro Lupoli +1
Noise-shaping quantization techniques are widely used for converting bandlimited signals from the analog to the digital domain. They work by ``shaping" the quantization noise so th…
How robust is randomized blind deconvolution via nuclear norm minimization against adversarial noise?
Julia Kostin, Felix Krahmer, Dominik Stöger
In this paper, we study the problem of recovering two unknown signals from their convolution, which is commonly referred to as blind deconvolution. Reformulation of blind deconvolu…
Uncertainty quantification for sparse Fourier recovery
Frederik Hoppe, Felix Krahmer, Claudio Mayrink Verdun +2
One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained -minimization. The m…
The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments
Dorian Florescu, Felix Krahmer, Ayush Bhandari
The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF allows…
Proof methods for robust low-rank matrix recovery
Tim Fuchs, David Gross, Peter Jung +3
Low-rank matrix recovery problems arise naturally as mathematical formulations of various inverse problems, such as matrix completion, blind deconvolution, and phase retrieval. Ove…
Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC
Ayush Bhandari, Felix Krahmer, Thomas Poskitt
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples…
The Modulo Radon Transform: Theory, Algorithms and Applications
Matthias Beckmann, Ayush Bhandari, Felix Krahmer
Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projectio…
On the robustness of noise-blind low-rank recovery from rank-one measurements
Felix Krahmer, Christian Kümmerle, Oleh Melnyk
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measure…
High order low-bit Sigma-Delta quantization for fusion frames
Zhen Gao, Felix Krahmer, Alexander M. Powell
We construct high order low-bit Sigma-Delta quantizers for the vector-valued setting of fusion frames. We prove that these quantizers can be stably implemented to quant…
Complex phase retrieval from subgaussian measurements
Felix Krahmer, Dominik Stöger
Phase retrieval refers to the problem of reconstructing an unknown vector or from measurements of the form $y_i = \big\vert \lang…
On Unlimited Sampling and Reconstruction
Ayush Bhandari, Felix Krahmer, Ramesh Raskar
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this…
On the convex geometry of blind deconvolution and matrix completion
Felix Krahmer, Dominik Stöger
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolutio…
On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds
Mark A. Iwen, Felix Krahmer, Sara Krause-Solberg +1
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manif…
Sparse Power Factorization: Balancing peakiness and sample complexity
Jakob Geppert, Felix Krahmer, Dominik Stöger
In many applications, one is faced with an inverse problem, where the known signal depends in a bilinear way on two unknown input vectors. Often at least one of the input vectors i…
Spectral Methods for Passive Imaging: Non-asymptotic Performance and Robustness
Kiryung Lee, Felix Krahmer, Justin Romberg
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of t…
On Unlimited Sampling
Ayush Bhandari, Felix Krahmer, Ramesh Raskar
Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set.…
Blind Demixing and Deconvolution at Near-Optimal Rate
Peter Jung, Felix Krahmer, Dominik Stöger
We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing…
Total Variation Minimization in Compressed Sensing
Felix Krahmer, Christian Kruschel, Michael Sandbichler
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the r…
Quantized Compressed Sensing for Partial Random Circulant Matrices
Joe-Mei Feng, Felix Krahmer, Rayan Saab
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies comp…
Empirical Chaos Processes and Blind Deconvolution
Ali Ahmed, Felix Krahmer, Justin Romberg
This paper investigates conditions under which certain kinds of systems of bilinear equations have a unique structured solution. In particular, we look at when we can recover vecto…
Phase Retrieval Without Small-Ball Probability Assumptions
Felix Krahmer, Yi-Kai Liu
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead…
Optimal Injectivity Conditions for Bilinear Inverse Problems with Applications to Identifiability of Deconvolution Problems
Michael Kech, Felix Krahmer
We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective o…
Noise-shaping Quantization Methods for Frame-based and Compressive Sampling Systems
Evan Chou, C. Sinan Güntürk, Felix Krahmer +2
Noise shaping refers to an analog-to-digital conversion methodology in which quantization error is arranged to lie mostly outside the signal spectrum by means of oversampling and f…