Exploring the solution space of linear inverse problems with GAN latent geometry

• URL: http://arxiv.org/abs/2207.00460v1
• Date: Fri, 1 Jul 2022 14:33:44 GMT
• Title: Exploring the solution space of linear inverse problems with GAN latent geometry
• Authors: Antonio Montanaro, Diego Valsesia, Enrico Magli
• Abstract summary: Inverse problems consist in reconstructing signals from incomplete sets of measurements. We propose a method to generate multiple reconstructions that fit both the measurements and a data-driven prior learned by a generative adversarial network.
• Score: 23.779985842891705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on obtaining a unique solution, an emerging trend considers exploring multiple feasibile solutions. In this paper, we propose a method to generate multiple reconstructions that fit both the measurements and a data-driven prior learned by a generative adversarial network. In particular, we show that, starting from an initial solution, it is possible to find directions in the latent space of the generative model that are null to the forward operator, and thus keep consistency with the measurements, while inducing significant perceptual change. Our exploration approach allows to generate multiple solutions to the inverse problem an order of magnitude faster than existing approaches; we show results on image super-resolution and inpainting problems.

Related papers

• The Differentiable Feasibility Pump [49.55771920271201]
  This paper shows that the traditional feasibility pump and many of its follow-ups can be seen as gradient-descent algorithms with specific parameters. A central aspect of this reinterpretation is observing that the traditional algorithm differentiates the solution of the linear relaxation with respect to its cost.
  arXiv  Detail & Related papers  (2024-11-05T22:26:51Z)
• Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency [7.671153315762146]
  Training diffusion models in the pixel space are both data-intensive and computationally demanding. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. We propose textitReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models.
  arXiv  Detail & Related papers  (2023-07-16T18:42:01Z)
• Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models [98.95988351420334]
  We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting.
  arXiv  Detail & Related papers  (2023-07-02T17:21:30Z)
• HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions [6.89453634946458]
  We propose homotopy physics-informed neural networks (HomPINNs) to solve inverse problems of nonlinear differential equations (DEs) The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters.
  arXiv  Detail & Related papers  (2023-04-06T01:20:23Z)
• Deep unfolding as iterative regularization for imaging inverse problems [6.485466095579992]
  Deep unfolding methods guide the design of deep neural networks (DNNs) through iterative algorithms. We prove that the unfolded DNN will converge to it stably. We demonstrate with an example of MRI reconstruction that the proposed method outperforms conventional unfolding methods.
  arXiv  Detail & Related papers  (2022-11-24T07:38:47Z)
• Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models [47.208080968675574]
  We study the use of generative models in inverse problems with more complete understanding. We support our claims with experimental results for solving various inverse problems. We propose an extension of our approach that can handle model mismatch (i.e., situations where the generative prior is not exactly applicable)
  arXiv  Detail & Related papers  (2021-05-13T15:58:27Z)
• Differentiable Causal Discovery from Interventional Data [141.41931444927184]
  We propose a theoretically-grounded method based on neural networks that can leverage interventional data. We show that our approach compares favorably to the state of the art in a variety of settings.
  arXiv  Detail & Related papers  (2020-07-03T15:19:17Z)
• Regularization of Inverse Problems by Neural Networks [0.0]
  Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their solutions. Deep learning techniques and neural networks demonstrated to significantly outperform classical solution methods for inverse problems.
  arXiv  Detail & Related papers  (2020-06-06T20:49:12Z)
• Solving Inverse Problems with a Flow-based Noise Model [100.18560761392692]
  We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns.
  arXiv  Detail & Related papers  (2020-03-18T08:33:49Z)
• Total Deep Variation for Linear Inverse Problems [71.90933869570914]
  We propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.
  arXiv  Detail & Related papers  (2020-01-14T19:01:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.