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Deterministic Compressed Sensing Matrices from Additive Character Sequences
Compressed sensing is a novel technique where one can recover sparse signals
from the undersampled measurements. In this correspondence, a
measurement matrix for compressed sensing is deterministically constructed via
additive character sequences. The Weil bound is then used to show that the
matrix has asymptotically optimal coherence for , and to present a
sufficient condition on the sparsity level for unique sparse recovery. Also,
the restricted isometry property (RIP) is statistically studied for the
deterministic matrix. Using additive character sequences with small alphabets,
the compressed sensing matrix can be efficiently implemented by linear feedback
shift registers. Numerical results show that the deterministic compressed
sensing matrix guarantees reliable matching pursuit recovery performance for
both noiseless and noisy measurements