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Found 13 papers, 1 papers with code
Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning
We develop a new data-driven approach for UQ in regression that applies both to classical regression approaches such as the LASSO as well as to neural networks.
High-Dimensional Confidence Regions in Sparse MRI
One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained $\ell_1$-minimization.
With or Without Replacement? Improving Confidence in Fourier Imaging
In this paper, we present a method to improve the debiased estimator by sampling without replacement.
The Mathematics of Dots and Pixels: On the Theoretical Foundations of Image Halftoning
A second class of methods that we discuss in detail is the class of error diffusion schemes, arguably among the most popular halftoning techniques due to their ability to work directly on a pixel grid and their ease of application.
Uncertainty quantification for learned ISTA
Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability.
Approximating Positive Homogeneous Functions with Scale Invariant Neural Networks
Furthermore, we also consider the approximation of general positive homogeneous functions with neural networks.
How robust is randomized blind deconvolution via nuclear norm minimization against adversarial noise?
Reformulation of blind deconvolution as a low-rank recovery problem has led to multiple theoretical recovery guarantees in the past decade due to the success of the nuclear norm minimization heuristic.
Non-intrusive surrogate modelling using sparse random features with applications in crashworthiness analysis
Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios.
Supervised dimensionality reduction
Uncertainty Quantification
The Modulo Radon Transform: Theory, Algorithms and Applications
Taking a computational imaging approach to the HDR tomography problem, we here suggest a new model based on the Modulo Radon Transform (MRT), which we rigorously introduce and analyze.
On the convex geometry of blind deconvolution and matrix completion
We find that for both these applications the dimension factors in the noise bounds are not an artifact of the proof, but the problems are intrinsically badly conditioned.
On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds
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 manifold of low intrinsic dimension.
Information Theory Information Theory
Are good local minima wide in sparse recovery?
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.
Stable and robust sampling strategies for compressive imaging
For Fourier measurements and Haar wavelet sparsity, the local coherence can be controlled and bounded explicitly, so for matrices comprised of frequencies sampled from a suitable inverse square power-law density, we can prove the restricted isometry property with near-optimal embedding dimensions.
