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Greedy Algorithms for Hybrid Compressed Sensing
Compressed sensing (CS) is a technique which uses fewer measurements than
dictated by the Nyquist sampling theorem. The traditional CS with linear
measurements achieves efficient recovery performances, but it suffers from the
large bit consumption due to the huge storage occupied by those measurements.
Then, the one-bit CS with binary measurements is proposed and saves the bit
budget, but it is infeasible when the energy information of signals is not
available as a prior knowledge. Subsequently, the hybrid CS which combines the
traditional CS and one-bit CS appears, striking a balance between the pros and
cons of both types of CS. Considering the fact that the one-bit CS is optimal
for the direction estimation of signals under noise with a fixed bit budget and
that the traditional CS is able to provide residue information and estimated
signals, we focus on the design of greedy algorithms, which consist of the main
steps of support detection and recovered signal update, for the hybrid CS in
this paper. We first propose a theorem on the random uniform tessellations for
sparse signals to further investigate the properties of one-bit CS. Afterwards,
we propose two greedy algorithms for the hybrid CS, with the one-bit CS
responsible for support detection and traditional CS offering updated residues
and signal estimates. For each of the proposed algorithms, we provide the
corresponding theorem with proof to analyze their capabilities theoretically.
Simulation results have demonstrated the efficacy of the proposed greedy
algorithms under a limited bit budget in noisy environments.Comment: 13 pages, 6 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl