A Deep Learning Approach to Structured Signal Recovery

Ali just sent me the following:

Dear Igor,

Recently, we have published a paper in which we have introduced a new approach for signal recovery from compressive measurements based on a deep learning approach.

I was thinking that it might be interesting for you and Nuit Blanche readers. The main point and innovation in our paper is that we can do the signal recovery with a great quality (outperforming almost all of the previous approaches) at least 1000 times faster. More specifically, we can recover an image from its compressive measurements in 0.002 seconds with a great quality.

You can find the paper in here:
http://arxiv.org/abs/1508.04065

Regards,
Ali

 Thanks Ali ! Table 1 and 2 are very telling but I chose to feature figure 8 of the paper as a reminder that the Great convergence will allow results in compressive sensing to yield interesting insights in Deep Learning. In particular, phase transitions are likely to provide good ways to evaluate the capabilities of this or that neural network architectures that ought to go faster than current reconstruction algorithms in compressive sensing (as shown in the following paper). Without further ado: A Deep Learning Approach to Structured Signal Recovery by Ali Mousavi, Ankit B. Patel, Richard G. Baraniuk

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach.

Related:

• Sunday Morning Insight: The Great Convergence ?
• Sunday Morning Insight: Randomization is not a dirty word
• Sunday Morning Insight: Sharp Phase Transitions in Machine Learning ?
• Sunday Morning Insight: Exploring Further the Limits of Admissibility
• Sunday Morning Insight: The Map Makers 
• Sunday Morning Insight: A Quick Panorama of Sensing from Direct Imaging to Machine Learning

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