Nur fatmawati
16611047
Nonuniform support recovery from noisy randon mesurements by Orthogonal Matching Persuit.
Compressive in sensing predicts
that sufficiently sparse vectors can recovered from highly incomplete
information. Efficient recovery methods such as ℓ1-minimization find the
sparsest solution to certain systems of equations. Random matrices have became
a popular choice for the measurement matrix. Indeed, near-optimal uniform
recovery results have been shown for such matrices. In this note nonuniform
recovery using Gaussian random matrices and ℓ1-minimization.Provide
a condition on the number of samples in terms of the sparsity and the signal
length which guarantees that a fixed sparse signal can be recovered with a
random draw of the matrix using ℓ1-minimization. The
constant 2 in the condition is optimal, and the proof is rather short compared
to a similar result due to Donoho and Tanner.
Admissible random measurements (of which Subgaussian measurements is
a special case) of fixed s-sparse signal x
in Rn corrupted
with additive noise, we show that under a condition on the minimum magnitude of
the nonzero components of x.
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