How to prevent frames on each groupplot in TikZ/pgfplots

I want to do a group of plots. However, I set the option \tikzset{every picture/.style={framed} at the begin of my document, because I want a frame around all my pictures. What I get now is a frame around the figure AND each subplot - which I don´t want. How can I prevent this?

MWE:

\documentclass{standalone}

\usepackage{pgfplots}
\usetikzlibrary{backgrounds,pgfplots.groupplots}

\tikzset{every picture/.style={framed,background rectangle/.style={draw=black!80,rounded corners=.5ex}}}

\begin{document}

\begin{tikzpicture}

\begin{groupplot}[group style={group size=2 by 2},
height=6cm, width=8cm,
xlabel=$\vartheta$,
hide y axis,
axis x line=middle,
xmin=-1, xmax=361,
every axis xlabel/.style={
at={(0,0)},anchor=center},
samples=200,
xtick={0,60, 120, 180, 240, 300, 360}]
\nextgroupplot[title={$m=0$}]
\nextgroupplot[title={$m=1$}]
\nextgroupplot[title={$m=2$}]
\nextgroupplot[title={$m=3$}]
\end{groupplot}

\end{tikzpicture}

\end{document}


Example (doesn´t look the as the MWE due to strange spacing in my document, but that shouldn´t bother):

Sorry if this question has already been asked or if there is an obvious answer - I couldn´t find anything.

-

You can pass the option /tikz/background rectangle/.style={draw=none} to groupplot (the prefix is required since those are TikZ keys):

\documentclass{standalone}

\usepackage{pgfplots}
\usetikzlibrary{backgrounds,pgfplots.groupplots}

\tikzset{
every picture/.style={
framed,
background rectangle/.style={
draw=black!80,
rounded corners=.5ex
}
}
}

\begin{document}

\begin{tikzpicture}

\begin{groupplot}[group style={group size=2 by 2},/tikz/background rectangle/.style={draw=none},
height=6cm, width=8cm,
xlabel=$\vartheta$,
hide y axis,
axis x line=middle,
xmin=-1, xmax=361,
every axis xlabel/.style={
at={(0,0)},anchor=center},
samples=200,
xtick={0,60, 120, 180, 240, 300, 360}]
\nextgroupplot[title={$m=0$}]
\nextgroupplot[title={$m=1$}]
\nextgroupplot[title={$m=2$}]
\nextgroupplot[title={$m=3$}]