Speckle-based X-ray phase contrast imaging (XPCI) is a relatively simple implementation of phase contrast imaging. At low energies, the technique has been demonstrated with masks made from steel wool and sandpaper. However, these materials are too transparent for higher energy applications. The simple geometry and easy identification of, or fabrication of, materials for relevant speckle masks make speckle-based XPCI a compelling technique for widespread use. We have analyzed the trade space for higher energy speckle-based XPCI systems based on portable X-ray tube sources. We have demonstrated several fabrication techniques compatible with a range of materials. Together these enable variation in feature size, material density, and randomness in the mask. This ability to tune the mask parameters allows optimization of the mask for the application space and system design.
KEYWORDS: Point spread functions, Compressed sensing, Super resolution, Signal to noise ratio, Reconstruction algorithms, Particles, Image resolution, Detection and tracking algorithms, Microscopy
Distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l1-norm, l0-norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. As a result, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.
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