  Speckle-based phase-contrast X-ray imaging (SB-PCXI) can reconstruct
high-resolution images of weakly-attenuating materials that would otherwise be
indistinguishable in conventional attenuation-based imaging. The experimental
setup of SB-PCXI requires only a sufficiently coherent source and spatially
random mask, positioned between the source and detector. The technique can
extract sample information at length scales smaller than the imaging system's
spatial resolution; this enables multimodal signal reconstruction. ``Multimodal
Intrinsic Speckle-Tracking'' (MIST) is a rapid and deterministic formalism
derived from the paraxial-optics form of the Fokker-Planck equation. MIST
simultaneously extracts attenuation, refraction, and small-angle scattering
(diffusive-dark-field) signals from a sample and is more computationally
efficient compared to alternative speckle-tracking approaches. Hitherto,
variants of MIST have assumed the diffusive-dark-field signal to be spatially
slowly varying. Although successful, these approaches have been unable to
well-describe unresolved sample microstructure whose statistical form is not
spatially slowly varying. Here, we extend the MIST formalism such that there is
no such restriction, in terms of a sample's rotationally-isotropic
diffusive-dark-field signal. We reconstruct multimodal signals of two samples,
each with distinct X-ray attenuation and scattering properties. The
reconstructed diffusive-dark-field signals have superior image quality compared
to our previous approaches which assume the diffusive-dark-field to be a slowly
varying function of transverse position. Our generalisation may assist
increased adoption of SB-PCXI in applications such as engineering and
biomedical disciplines, forestry, and palaeontology, and is anticipated to aid
the development of speckle-based diffusive-dark-field tensor tomography.
