Low-exposure high-quality multimodal speckle x-ray imaging via an intrinsic gradient-flow approach

We present an approach for retrieving dark-field, phase-shift, and attenuation images from speckle-based x-ray imaging data. Speckle-based x-ray imaging (SBXI) exploits sample-induced alterations to a reference near-field speckle pattern produced by a randomly structured mask. Attenuation images allow materials of different densities to be visualized. Phase-shift images are useful because they reveal how materials in a sample refract the x-ray beam, providing contrast between similar low-density structures that are difficult to reconstruct in attenuation images. Dark-field images convey information about structures that are smaller than the spatial resolution and are thus invisible in both attenuation and phase-shift images. In previous works, we presented the multimodal intrinsic speckle-tracking (MIST) algorithm, which recovers the three complementary images from SBXI data by solving the associated x-ray Fokker-Planck equation. In this work, we present a variation of MIST, which we call ``gradient-flow MIST,'' which (1) reduces the amount of SBXI data required for image retrieval, (2) maintains the full generality of the x-ray Fokker-Planck equation, and (3) recovers dark-field images with higher quality than the previously proposed variants for weakly attenuating (i.e., low density) samples. We demonstrate the new gradient-flow MIST approach on experimental SBXI data of a knotted bundle of carbon fibers acquired at the Australian synchrotron. This approach is anticipated to be useful in phase-contrast and dark-field applications that require simplicity in experimentation and low sample x-ray exposure.