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Found 12 papers, 2 papers with code
The Star Geometry of Critic-Based Regularizer Learning
Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizers via deep neural networks showcasing impressive empirical performance.
Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching
We validate our approach for various linear inverse problems, such as super-resolution, deblurring, inpainting, and compressed sensing, and demonstrate that we can outperform other methods based on flow matching.
Score-Based Diffusion Models for Photoacoustic Tomography Image Reconstruction
Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth.
Discovering Structure From Corruption for Unsupervised Image Reconstruction
We show that such a set of inverse problems can be solved simultaneously without the use of a spatial image prior by instead inferring a shared image generator with a low-dimensional latent space.
Image Reconstruction without Explicit Priors
We show that such a set of inverse problems can be solved simultaneously by learning a shared image generator with a low-dimensional latent space.
Optimal Regularization for a Data Source
In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what is the optimal regularizer for data drawn from the distribution?
Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval
Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements.
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.
Low Shot Learning with Untrained Neural Networks for Imaging Inverse Problems
In particular, how can one use the availability of a small amount of data (even $5-25$ examples) to one's advantage in solving these inverse problems and can a system's performance increase as the amount of data increases as well?
Invertible generative models for inverse problems: mitigating representation error and dataset bias
For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images.
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.
