The cross-section of an X-ray phase shift image is a thousand times greater than that of X-ray attenuation in soft tissue over the diagnostic energy range implying phase imaging can achieve a much higher signal-to-noise ratio and substantially lower radiation dose than attenuation-based X-ray imaging. Grating interferometry is a state of the art X-ray imaging approach, which can simultaneously acquire information of X-ray phase-contrast, dark-field, and linear attenuation. This imaging modality can reveal subtle texture of tissues. For example, the growth of tumors causes remarkable differences of small-angle scattering patterns from that of healthy tissues. It is clinically important that the structural variation in tumor modifies the refractive index; however, conventional grating interferometers often use flat gratings, with serious limitations in the field of view and the flux of photons. This invention provides novel and advantageous systems and methods for X-ray phase-contrast imaging (PCI), including the use of one or more period-varying or quasi-periodic gratings. This X-ray PCI system can include a phase grating that is period-varying or quasi-periodic and can be positioned between an object being imaged and a detector. A second grating, such as an absorption grating or an analyzer grating can also be present and disposed between the phase grating and the detector. The subject invention also provides second-order approximation models for X-ray phase retrieval, for example using paraxial Fresnel-Kirchhoff diffraction theory. An iterative method can be used to reconstruct a phase-contrast image andor a dark-field image. The models can be iteratively solved using the algebraic reconstruction technique (ART). State of the art compressive sensing techniques can be incorporated to achieve high quality image reconstruction.