Learning to Invert: Signal Recovery via Deep Convolutional Networks

As mentioned for a while now, compressive sensing's Achille's heel is related to how slow reconstruction solvers are (see Sunday Morning Insight: Faster Than a Blink of an Eye). The following paper attempts to use the techniques of deep neural networks to learning the transformation we generally associate with reconstruction solvers in a scheme called 'Learning to invert'. I like the sound of that great convergence in action !

Learning to Invert: Signal Recovery via Deep Convolutional Networks by Ali Mousavi, Richard G. Baraniuk

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.

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