In-line　digital　holography　offers　the　advantages　of　compact　layout　and　full　utilization　of　the　spatial　bandwidth　product　of　the　detector,　making　it　widely　used　in　the　terahertz　band.　In　this　paper,　we　propose　an　extrapolated　iterative　algorithm　that　combines　the　object＇s　absorption　characteristics　with　the　sparsity　of　the　complex　field,　enabling　high-fidelity　retrieval　of　both　amplitude　and　phase　images　from　a　single　in-line　hologram.　At　the　same　time,　the　size　of　the　hologram　is　numerically　expanded　without　increasing　the　system　complexity　or　the　data　acquisition　time.　The　effectiveness　of　this　algorithm　is　demonstrated　through　high-quality　imaging　of　a　Siemens　star,　polypropylene　sheet,　and　dragonfly　hindwing.　Compared　with　the　phase　retrieval　algorithm　which　includes　positive　absorption　constraint,　extrapolation　method　and　support　domain　constraint,　our　method　achieves　superior　reconstruction　quality　and　more　effective　twin-image　suppression,　enhancing　the　resolution　from　310　mu　m　(2.67)　to　228　mu　m　(1.97)　and　enabling　high-fidelity　reconstruction　of　a　30　mu　m　dragonfly　hindwing.　This　work　will　further　enhance　the　application　of　continuous-wave　terahertz　in-line　digital　holography　in　biomedical　imaging　and　non-destructive　testing.