论文标题
通过$ \ ell_1 $最小化的稀疏信号的仿射阶段检索
Affine phase retrieval for sparse signals via $\ell_1$ minimization
论文作者
论文摘要
仿射相的检索是通过先验信息从仅幅度测量值中恢复信号的问题。在本文中，我们使用$ \ ell_1 $最小化来利用信号的偏见量检索，这表明$ o（k \ log（en/k））$高斯随机测量足以恢复所有$ k $ -s-sparse信号，通过解决一个天然$ \ ell_1 $ \ ell_1 $ \ ell_1 $ nes $ n $ n $ n ins n dimemension nes dimemension。对于在噪音损坏测量的情况下，对实价和复杂值的信号给出了重建误差界限。我们的结果表明，天然的$ \ ell_1 $最小化程序用于仿射期检索是稳定的。
Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the $\ell_1$ minimization to exploit the sparsity of signals for affine phase retrieval, showing that $O(k\log(en/k))$ Gaussian random measurements are sufficient to recover all $k$-sparse signals by solving a natural $\ell_1$ minimization program, where $n$ is the dimension of signals. For the case where measurements are corrupted by noises, the reconstruction error bounds are given for both real-valued and complex-valued signals. Our results demonstrate that the natural $\ell_1$ minimization program for affine phase retrieval is stable.
