Learning to Invert: Signal Recovery via Deep Convolutional Networks

TL;DR

This paper introduces DeepInverse, a deep convolutional network framework that learns to invert measurement processes for compressive sensing, achieving near state-of-the-art accuracy with significantly faster recovery times.

Contribution

The paper presents a novel deep learning-based approach for signal recovery in compressive sensing that learns the inverse transformation, combining accuracy with ultrafast inference.

Findings

DeepInverse closely matches state-of-the-art recovery algorithms.

It achieves hundreds of times faster inference speed.

Training is computationally intensive but only needs to be done once.

Abstract

The promise of compressive sensing (CS) has been offset by two significant challenges. First, real-world data is not exactly sparse in a fixed basis. Second, current high-performance recovery algorithms are slow to converge, which limits CS to either non-real-time applications or scenarios where massive back-end computing is available. In this paper, we attack both of these challenges head-on by developing a new signal recovery framework we call {\em DeepInverse} that learns the inverse transformation from measurement vectors to signals using a {\em deep convolutional network}. When trained on a set of representative images, the network learns both a representation for the signals (addressing challenge one) and an inverse map approximating a greedy or convex recovery algorithm (addressing challenge two). Our experiments indicate that the DeepInverse network closely approximates the solution produced by state-of-the-art CS recovery algorithms yet is hundreds of times faster in run time. The tradeoff for the ultrafast run time is a computationally intensive, off-line training procedure typical to deep networks. However, the training needs to be completed only once, which makes the approach attractive for a host of sparse recovery problems.