Acquisition of a single grid-based phase-contrast X-ray image using instantaneous frequency and noise filtering.

"Declarations Ethics approval and consent to participateNot applicable. Consent for publicationNot applicable. Competing interestsNot applicable. Competing interests Not applicable."

"Funding This work was partly supported by the Technology development Program of MSS [S3146559], the National Research Foundation of Korea (NRF) Grants funded by the Korean government (MSIP: Ministry of Science, ICT, and Future Planning; No. NRF-2022R1A2C1092072), and by the Korea Medical Device Development Fund grant funded by the Korea government (the Ministry of Science and ICT, the Ministry of Trade, Industry and Energy, the Ministry of Health & Welfare, the Ministry of Food and Drug Safety) (Project Number: 1711174276, RS-2020-KD000016). The funders had no role in study design, data collection and analysis, decision to publish, or manuscript preparation."