In this work, we investigate the problem of simultaneous blind demixing and super-resolution. Leveraging the subspace assumption regarding unknown point spread functions, this problem can be reformulated as a low-rank matrix demixing problem. We propose a convex recovery approach that utilizes the low-rank structure of each vectorized Hankel matrix associated with the target matrix. Our analysis reveals that for achieving exact recovery, the number of samples needs to satisfy the condition $n\gtrsim Ksr \log (sn)$. Empirical evaluations demonstrate the recovery capabilities and the computational efficiency of the convex method.

翻译：本文研究了同步盲解混和超分辨率的联合问题。利用未知点扩展函数的子空间假设，该问题可被重新表述为低秩矩阵分解问题。我们提出了一种凸恢复方法，该方法利用了与目标矩阵相关联的每个向量化汉克尔矩阵的低秩结构。理论分析表明，为实现精确恢复，样本数量需满足条件$n\gtrsim Ksr \log (sn)$。实验评估验证了该凸方法的恢复能力与计算效率。