DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networks
This work addresses the challenge of efficient signal recovery for applications like imaging or communications, though it is incremental as it builds on existing compressive sensing with deep learning enhancements.
The paper tackles the problem of sensing and recovering structured signals by developing a deep learning framework that learns to take undersampled measurements and recover signals, outperforming traditional compressive sensing methods like ℓ1-minimization in phase transition regions where the latter fails.
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.