Underwater　image　enhancement,　especially　in　color　restoration　and　detail　reconstruction,　remains　a　significant　challenge.　Current　models　focus　on　improving　accuracy　and　learning　efficiency　through　neural　network　design,　often　neglecting　traditional　optimization　algorithms＇　benefits.　We　propose　FAIN-UIE,　a　novel　approach　for　color　and　fine-texture　recovery　in　underwater　imagery.　It　leverages　insights　from　the　Fast　Iterative　Shrink-Threshold　Algorithm　(FISTA)　to　approximate　image　degradation,　enhancing　network　fitting　speed.　FAIN-UIE　integrates　the　residual　degradation　module　(RDM)　and　momentum　calculation　module　(MC)　for　gradient　descent　and　momentum　simulation,　addressing　feature　fusion　losses　with　the　Feature　Merge　Block　(FMB).　By　integrating　multi-scale　information　and　inter-stage　pathways,　our　method　effectively　maps　multi-stage　image　features,　advancing　color　and　fine-texture　restoration.　Experimental　results　validate　its　robust　performance,　positioning　FAIN-UIE　as　a　competitive　solution　for　practical　underwater　imaging　applications.