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Found 12 papers, 1 papers with code
Optimal Sample Complexity of Subgradient Descent for Amplitude Flow via Non-Lipschitz Matrix Concentration
We establish local convergence of subgradient descent with optimal sample complexity based on the uniform concentration of a random, discontinuous matrix-valued operator arising from the objective's gradient dynamics.
Compressive Phase Retrieval: Optimal Sample Complexity with Deep Generative Priors
Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with potentially fundamental sample complexity bottlenecks.
Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors
Many problems in statistics and machine learning require the reconstruction of a rank-one signal matrix from noisy data.
Deep Denoising: Rate-Optimal Recovery of Structured Signals with a Deep Prior
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 image.
Phase Retrieval Under a Generative Prior
Our formulation has provably favorable global geometry for gradient methods, as soon as $m = O(kd^2\log n)$, where $d$ is the depth of the network.
Rate-Optimal Denoising with Deep Neural Networks
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.
Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk
We establish that in both cases, in suitable regimes of network layer sizes and a randomness assumption on the network weights, that the non-convex objective function given by empirical risk minimization does not have any spurious stationary points.
A Survey of Structure from Motion
The structure from motion (SfM) problem in computer vision is the problem of recovering the three-dimensional ($3$D) structure of a stationary scene from a set of projective measurements, represented as a collection of two-dimensional ($2$D) images, via estimation of motion of the cameras corresponding to these images.
ShapeFit and ShapeKick for Robust, Scalable Structure from Motion
We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers.
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue.
Optimization and Control Numerical Analysis
Exact simultaneous recovery of locations and structure from known orientations and corrupted point correspondences
This recovery theorem is based on a set of deterministic conditions that we prove are sufficient for exact recovery.
ShapeFit: Exact location recovery from corrupted pairwise directions
We prove that this program recovers a set of $n$ i. i. d.
