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This letter investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavy-tailed impulsive noise is well modeled with stable distributions. Since there is no explicit formula for the probability density function of SαS distribution, alternative approximations are used, such as, generalized Gaussian distribution, which imposes ℓp-norm fidelity on the residual error. In this letter, we exploit a continuous mixed norm (CMN) for robust sparse recovery instead of ℓp-norm. We show that in blind conditions, i.e., in the case where the parameters of the noise distribution are unknown, incorporating CMN can lead to near-optimal recovery. We apply...