3 research outputs found
Noise Variance Estimation Using Asymptotic Residual in Compressed Sensing
In compressed sensing, the measurement is usually contaminated by additive
noise, and hence the information of the noise variance is often required to
design algorithms. In this paper, we propose an estimation method for the
unknown noise variance in compressed sensing problems. The proposed method
called asymptotic residual matching (ARM) estimates the noise variance from a
single measurement vector on the basis of the asymptotic result for the
optimization problem. Specifically, we derive the asymptotic
residual corresponding to the optimization and show that it depends
on the noise variance. The proposed ARM approach obtains the estimate by
comparing the asymptotic residual with the actual one, which can be obtained by
the empirical reconstruction without the information of the noise variance.
Simulation results show that the proposed noise variance estimation outperforms
a conventional method based on the analysis of the ridge regularized least
squares. We also show that, by using the proposed method, we can achieve good
reconstruction performance in compressed sensing even when the noise variance
is unknown.Comment: This work has been submitted to the IEEE for possible publication.
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