A　set　of　wavelet　frames　generated　by　Gaussian　radial　basis　functions　are　presented.　It　is　constructively　proved　that　a　radial　basis　function　network　with　Gaussian　activation　functions　can　approximate　any　function　in　L2(Rd)　with　desired　accuracy.　Furthermore,　an　adaptive　learning　algorithm　of　constructing　and　training　networks　is　proposed　based　on　time-frequency　localization　properties　of　Gaussian　radial　basis　functions　and　the　adaptive　projection　algorithm.　Applications　to　signal　reconstruction　and　noise　elimination　are　given.