DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networks

TL;DR

DeepCodec introduces a deep learning-based framework that learns to take undersampled measurements and recover structured signals, outperforming traditional compressive sensing methods in phase transition and efficiency.

Contribution

It presents a novel neural network approach for adaptive sensing and recovery, replacing traditional random measurements and optimization with learned transformations.

Findings

Outperforms $$-minimization in phase transition regions.

Learning measurements improves recovery performance and training speed.

Fewer parameters are needed for the neural network.

Abstract

In this paper we develop a novel computational sensing framework for sensing and recovering structured signals. When trained on a set of representative signals, our framework learns to take undersampled measurements and recover signals from them using a deep convolutional neural network. In other words, it learns a transformation from the original signals to a near-optimal number of undersampled measurements and the inverse transformation from measurements to signals. This is in contrast to traditional compressive sensing (CS) systems that use random linear measurements and convex optimization or iterative algorithms for signal recovery. We compare our new framework with $\ell_1$-minimization from the phase transition point of view and demonstrate that it outperforms $\ell_1$-minimization in the regions of phase transition plot where $\ell_1$-minimization cannot recover the exact solution. In addition, we experimentally demonstrate how learning measurements enhances the overall recovery performance, speeds up training of recovery framework, and leads to having fewer parameters to learn.