# Learning Generative Prior with Latent Space Sparsity Constraints

arXiv: https://arxiv.org/abs/2105.11956 · HTML: https://mlsanity.com/paper/2105.11956/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 24 of 24)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Image Processing Using Multi-Code GAN Prior](https://mlsanity.com/paper/1912.07116/) (2019)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [DeLiGAN : Generative Adversarial Networks for Diverse and Limited Data](https://mlsanity.com/paper/1706.02071/) (2017)
- [Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees](https://mlsanity.com/paper/1802.08406/) (2018)
- [Deep Compressed Sensing](https://mlsanity.com/paper/1905.06723/) (2019)
- [Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk](https://mlsanity.com/paper/1705.07576/) (2017)
- [Image-Adaptive GAN based Reconstruction](https://mlsanity.com/paper/1906.05284/) (2019)
- [Modeling Sparse Deviations for Compressed Sensing using Generative Models](https://mlsanity.com/paper/1807.01442/) (2018)
- [Disconnected Manifold Learning for Generative Adversarial Networks](https://mlsanity.com/paper/1806.00880/) (2018)
- [Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models](https://mlsanity.com/paper/1908.10744/) (2019)
- [Compressible Latent-Space Invertible Networks for Generative Model-Constrained Image Reconstruction](https://mlsanity.com/paper/2007.02462/) (2020)
- [Learning Sparse Latent Representations with the Deep Copula Information Bottleneck](https://mlsanity.com/paper/1804.06216/) (2018)
- [Latent Convolutional Models](https://mlsanity.com/paper/1806.06284/) (2018)
- [Fast Compressive Sensing Recovery Using Generative Models with Structured Latent Variables](https://mlsanity.com/paper/1902.06913/) (2019)
- [Learning optimal nonlinearities for iterative thresholding algorithms](https://mlsanity.com/paper/1512.04754/) (2015)
- [Subspace Embeddings Under Nonlinear Transformations](https://mlsanity.com/paper/2010.02264/) (2020)

## Built on by (most cited first, 1 of 1)

- [The Essential Role of Causality in Foundation World Models for Embodied AI](https://mlsanity.com/paper/2402.06665/) (2024)

## Abstract (arXiv)

We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural network. Recently, it has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. SDLSS allows the range-space of the generator to be considered as a union-of-submanifolds. We also derive the sample complexity bounds within the SDLSS framework for the linear measurement model. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method. We first consider a comparison between linear and nonlinear sensing mechanisms on Fashion-MNIST dataset and show that the learned nonlinear version is superior to the linear one. Subsequent comparisons with the deep compressive sensing (DCS) framework proposed in the literature are reported. We also consider the effect of the dimension of the latent space and the sparsity factor in validating the SDLSS framework. Performance quantification is carried out by employing three objective metrics: peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and reconstruction error (RE).