4,242 research outputs found
Measure What Should be Measured: Progress and Challenges in Compressive Sensing
Is compressive sensing overrated? Or can it live up to our expectations? What
will come after compressive sensing and sparsity? And what has Galileo Galilei
got to do with it? Compressive sensing has taken the signal processing
community by storm. A large corpus of research devoted to the theory and
numerics of compressive sensing has been published in the last few years.
Moreover, compressive sensing has inspired and initiated intriguing new
research directions, such as matrix completion. Potential new applications
emerge at a dazzling rate. Yet some important theoretical questions remain
open, and seemingly obvious applications keep escaping the grip of compressive
sensing. In this paper I discuss some of the recent progress in compressive
sensing and point out key challenges and opportunities as the area of
compressive sensing and sparse representations keeps evolving. I also attempt
to assess the long-term impact of compressive sensing
Hamming Compressed Sensing
Compressed sensing (CS) and 1-bit CS cannot directly recover quantized
signals and require time consuming recovery. In this paper, we introduce
\textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit
quantized signal of dimensional from its 1-bit measurements via invoking
times of Kullback-Leibler divergence based nearest neighbor search.
Compared with CS and 1-bit CS, HCS allows the signal to be dense, takes
considerably less (linear) recovery time and requires substantially less
measurements (). Moreover, HCS recovery can accelerate the
subsequent 1-bit CS dequantizer. We study a quantized recovery error bound of
HCS for general signals and "HCS+dequantizer" recovery error bound for sparse
signals. Extensive numerical simulations verify the appealing accuracy,
robustness, efficiency and consistency of HCS.Comment: 33 pages, 8 figure
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