Amortized Variational Compressive Sensing

The goal of statistical compressive sensing is to efficiently acquire and reconstruct high-dimensional signals with much fewer measurements, given access to a finite set of training signals from the underlying domain being sensed. We present a novel algorithmic framework based on autoencoders that jointly learns the acquisition (a.k.a. encoding) and recovery (a.k.a. decoding) functions while implicitly modeling domain structure. Our learning objective maximizes a variational lower bound to the mutual information between the signal and the measurements. Empirically, we show 20− 46% improvement in reconstruction accuracies over competing approaches on the MNIST dataset for the same number of measurements.