  After the recent discovery of a Standard Model Higgs boson-like particle at
the LHC, the question of its couplings to known and unknown matter is eminent.
In this letter, we present a method that allows for an enhancement in
S/B(irreducible) of the order of 100% in $pp\to (h\to \gamma\gamma) jj$ for a
center of mass energy of 8 and 14 TeV. This is achieved by applying the matrix
element method. We discuss the implications of detector resolution effects and
various approximations of the involved event simulation and reconstruction. The
matrix element method provides a reliable, stable, and efficient handle to
separate signal from background, and the gluon and weak boson fusion components
involved in this process. Employing this method, a more precise Higgs boson
coupling extraction can be obtained, and our results are of immediate relevance
for current searches.
