Perhaps something like this:

I let tikzpagenodes do the math so that you can change all the settings you want in geometry and fancyhdr such as top or headersep and so on. You will need to compile twice:
\documentclass{report}
\usepackage{fancyhdr}
\usepackage[left=4cm,top=10cm,right=3cm,bottom=3cm]{geometry}
\pagestyle{fancy}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{tikzpagenodes}
\renewcommand{\headrulewidth}{0pt}
\lhead{\begin{tikzpicture}[remember picture,overlay]
\draw let \p1=($(current page.north)-(current page header area.south)$),
\n1={veclen(\x1,\y1)} in
node [inner sep=0,outer sep=0,below right]
at (current page.north west){\includegraphics[width=\paperwidth,height=\n1]{img}};
\end{tikzpicture}}
\begin{document}
\section{First section}
Type your document as usual!
\newpage
\section{Second section}
Type your document as usual!
\end{document}
I had trouble finding the distance between the header text and the headrule, so I've zeroed its thickness as I thought you won't need it.