Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability and Instance Optimality for Gaussian Measurements in Compressed Sensing
Foundations of Computational Mathematics
Compressive Sensing by Random Convolution
SIAM Journal on Imaging Sciences
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Efficient measurement generation and pervasive sparsity for compressive data gathering
IEEE Transactions on Wireless Communications
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Compressive sensing provides a framework for recovering sparse signals of length N from M ≪ N measurements. If the measurements contain noise bounded by ε, then standard algorithms recover sparse signals with error at most Cε. However, these algorithms perform suboptimally when the measurement noise is also sparse. This can occur in practice due to shot noise, malfunctioning hardware, transmission errors, or narrowband interference. We demonstrate that a simple algorithm, which we dub Justice Pursuit (JP), can achieve exact recovery from measurements corrupted with sparse noise. The algorithm handles unbounded errors, has no input parameters, and is easily implemented via standard recovery techniques.