Robust reconstruction under unknown SNR signal for analog-to-information conversion

A robust method to reconstruct the spectrum information for the analog-to-information converter (AIC) is developed. Current reconstruction algorithms require the prior knowledge or the estimation of noise level to set algorithmic parameters and stopping conditions. The proposed method requires no knowledge of noises or the acquired signal-to-noise ratio (SNR). We present a joined convex optimization model (JCO). Sampling at half of the Nyquist rate, the information of the origin signal can be rebuilt under the SNR as low as -10dB.