[Paper Review] Deep Compressed Sensing

Yan Wu, Mihaela Rosca+1 more|arXiv (Cornell University)|May 16, 2019

Sparse and Compressive Sensing Techniques58 citations

TL;DR

The paper introduces Deep Compressed Sensing (DCS), training both measurements and reconstruction networks end-to-end with meta-learning, improving speed and accuracy over previous CS methods and enabling GAN variants via learned measurement objectives.

ABSTRACT

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.

Motivation & Objective

• Motivate the limitations of traditional compressed sensing (sparsity assumption and slow reconstruction).
• Develop a framework that trains both measurement functions and a neural network generator within CS to improve reconstruction speed and accuracy.
• Show how meta-learning can accelerate latent optimization for reconstruction.
• Derive and evaluate a family of models, including CS-GAN and CS-SGAN, using learned measurements and discriminator/ classifier guidance.

Proposed method

• Formulate Deep Compressed Sensing (DCS) by jointly training a generator G_theta and the reconstruction latent optimization process.
• Enforce distance-preserving properties (RIP-like) via a measurement loss L_F to train F_phi and/or learn F_phi as a neural network.
• Incorporate model-agnostic meta-learning (MAML-style) to back-propagate through latent optimization steps, reducing the number of gradient steps needed.
• Derive CS-GAN by replacing the measurement loss with a discriminator-guided objective, linking latent optimization to GAN training.
• Extend to CS-SGAN by using a multi-class classifier to preserve class information in measurements, enabling semi-supervised GAN behavior.
• Provide algorithms (Algorithm 1 and Algorithm 2) for training with either fixed or learned measurement functions.

Experimental results

Research questions

• RQ1 Can meta-learning of the latent optimization process accelerate reconstruction in deep compressed sensing compared with standard gradient descent approaches?
• RQ2 Does enforcing a RIP-like property via learnable measurements improve reconstruction quality over random measurements, and under what conditions?
• RQ3 Can latent optimization guided by a discriminator improve GAN training stability and sample quality, compared to vanilla GANs?
• RQ4 Can the DCS framework be extended to semi-supervised GANs to produce semantically meaningful latent spaces?
• RQ5 What is the effect of learned measurement functions on reconstruction and GAN performance for image data such as MNIST and CelebA?

Key findings

• DCS significantly improves reconstruction performance over the Bora et al. baseline, while using far fewer latent optimization steps (3 steps) without re-starts.
• Learned measurement functions outperform random projections when optimized, and neural measurement models can further improve results, particularly for structured data like images.
• Latent optimization within CS-GANs leads to better GAN metrics (IS and FID) and avoids mode collapse more effectively than vanilla GANs, with improvements sustained across a range of hyper-parameters.
• CS-GANs with latent optimization can outperform a strong baseline (SN-GAN) and achieve competitive results when combined with spectral normalization and larger architectures.
• CS-SGAN demonstrates that latent optimization yields a semantically structured latent space, enabling clearer class separation in generated samples (e.g., MNIST digits).
• The paper provides a unified framework where GANs emerge as a special case of measurements that preserve certain properties (validity preservation or class preservation) within the DCS paradigm.