Affine phase retrieval for sparse signals via ℓ1\ell_1 minimization

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.Comment: 22 page

Patterned nanofiber air filters with high optical transparency, robust mechanical strength, and effective PM_(2.5) capture capability

PM_(2.5), due to its small particle size, strong activity, ease of the attachment of toxic substances and long residence time in the atmosphere, has a great impact on human health and daily production. In this work, we have presented patterned nanofiber air filters with high optical transparency, robust mechanical strength and effective PM_(2.5) capture capability. Here, to fabricate a transparency air filter by a facile electrospinning method, we chose three kinds of patterned wire meshes with micro-structures as negative receiver substrates and directly electrospun polymer fibers onto the supporting meshes. Compared with randomly oriented nanofibers (named “RO NFs” in this paper) and commercially available facemasks, the patterned air filters showed great mechanical properties, and the water contact angles on their surfaces were about 122–143° (the water contact angle for RO NFs was 81°). In addition, the patterned nanofibers exhibited high porosity (>80%), and their mean pore size was about 0.5838–0.8686 μm (the mean pore size of RO NFs was 0.4374 μm). The results indicate that the transparent patterned air filters have the best PM_(2.5) filtration efficiency of 99.99% at a high transmittance of ∼69% under simulated haze pollution

Patterned nanofiber air filters with high optical transparency, robust mechanical strength, and effective PM_(2.5) capture capability

PM_(2.5), due to its small particle size, strong activity, ease of the attachment of toxic substances and long residence time in the atmosphere, has a great impact on human health and daily production. In this work, we have presented patterned nanofiber air filters with high optical transparency, robust mechanical strength and effective PM_(2.5) capture capability. Here, to fabricate a transparency air filter by a facile electrospinning method, we chose three kinds of patterned wire meshes with micro-structures as negative receiver substrates and directly electrospun polymer fibers onto the supporting meshes. Compared with randomly oriented nanofibers (named “RO NFs” in this paper) and commercially available facemasks, the patterned air filters showed great mechanical properties, and the water contact angles on their surfaces were about 122–143° (the water contact angle for RO NFs was 81°). In addition, the patterned nanofibers exhibited high porosity (>80%), and their mean pore size was about 0.5838–0.8686 μm (the mean pore size of RO NFs was 0.4374 μm). The results indicate that the transparent patterned air filters have the best PM_(2.5) filtration efficiency of 99.99% at a high transmittance of ∼69% under simulated haze pollution