Neural　networks　that　are　embedded　with　prior　knowledge　of　the　distribution　of　the　original　signal　in　applications　of　compressed　sensing　have　attracted　increasing　attention.　However,　the　maximal　probability　of　the　desired　output　by　a　neural　network　cannot　guarantee　that　the　statistical　distribution　of　the　recovered　signal　is　consistent　with　the　statistical　distribution　of　the　original　signal.　In　this　paper,　we　combine　neural　networks　with　information　geometry　to　study　the　recovery　of　sparse　signals　that　satisfy　a　certain　distribution.　We　construct　the　geodesic　distance　between　the　distribution　of　the　original　signal　and　distribution　of　the　recovered　signal　as　the　input　for　the　neural　network.　Experiments　show　that　the　proposed　method　has　a　better　reconstruction　quality　compared　with　existing　algorithms.