Lochocki Benjamin, Abrashitova Ksenia, de Boer Johannes F, Amitonova Lyubov V
Opt Express. 2021 Feb 1;29(3):3943-3955. doi: 10.1364/OE.413831.
Compressive imaging using sparsity constraints is a very promising field of microscopy that provides a dramatic enhancement of the spatial resolution beyond the Abbe diffraction limit. Moreover, it simultaneously overcomes the Nyquist limit by reconstructing an N-pixel image from less than N single-point measurements. Here we present fundamental resolution limits of noiseless compressive imaging via sparsity constraints, speckle illumination and single-pixel detection. We addressed the experimental setup that uses randomly generated speckle patterns (in a scattering media or a multimode fiber). The optimal number of measurements, the ultimate spatial resolution limit and the surprisingly important role of discretization are demonstrated by the theoretical analysis and numerical simulations. We show that, in contrast to conventional microscopy, oversampling may decrease the resolution and reconstruction quality of compressive imaging.
利用稀疏约束的压缩成像在显微镜领域是一个非常有前景的方向，它能显著提高空间分辨率，超越阿贝衍射极限。此外，它还能通过少于N次单点测量重建N像素图像，从而同时克服奈奎斯特极限。在此，我们给出了基于稀疏约束、散斑照明和单像素检测的无噪声压缩成像的基本分辨率极限。我们探讨了使用随机生成散斑图案（在散射介质或多模光纤中）的实验装置。理论分析和数值模拟证明了测量的最佳数量、最终空间分辨率极限以及离散化出人意料的重要作用。我们表明，与传统显微镜不同，过采样可能会降低压缩成像的分辨率和重建质量。
