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DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees

arXiv 2101.05130 ↗First posted 13 Jan 2021eess.IV cs.CV cs.LGcited by 0

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Abstract (arXiv)

Generative priors have been shown to provide improved results over sparsity priors in linear inverse problems. However, current state of the art methods suffer from one or more of the following drawbacks: (a) speed of recovery is slow; (b) reconstruction quality is deficient; (c) reconstruction quality is contingent on a computationally expensive process of tuning hyperparameters. In this work, we address these issues by utilizing Denoising Auto Encoders (DAEs) as priors and a projected gradient descent algorithm for recovering the original signal. We provide rigorous theoretical guarantees for our method and experimentally demonstrate its superiority over existing state of the art methods in compressive sensing, inpainting, and super-resolution. We find that our algorithm speeds up recovery by two orders of magnitude (over 100x), improves quality of reconstruction by an order of magnitude (over 10x), and does not require tuning hyperparameters.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 45 references that are in the map. First posted on arXiv 13 Jan 2021.

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21 of 45 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2017Compressed Sensing using Generative Modelscited by 337
  4. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  5. 2016Semantic Image Inpainting with Deep Generative Modelscited by 156
  6. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  7. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  8. 2013Generalized Denoising Auto-Encoders as Generative Modelscited by 113
  9. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  10. 2017CNN-Based Projected Gradient Descent for Consistent Image Reconstructioncited by 75
  11. 2016Amortised MAP Inference for Image Super-resolutioncited by 68
  12. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
9 more
  1. 2017Learned D-AMP: Principled Neural Network based Compressive Image Recoverycited by 65
  2. 2018Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guaranteescited by 58
  3. 2018Neural Proximal Gradient Descent for Compressive Imagingcited by 46
  4. 2017When Image Denoising Meets High-Level Vision Tasks: A Deep Learning Approachcited by 42
  5. 2020Provable Convergence of Plug-and-Play Priors with MMSE denoiserscited by 39
  6. 2019Algorithmic Guarantees for Inverse Imaging with Untrained Network Priorscited by 32
  7. 2017Learning to Invert: Signal Recovery via Deep Convolutional Networkscited by 22
  8. 2017DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networkscited by 8
  9. 2017An inner-loop free solution to inverse problems using deep neural networkscited by 1

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