In this letter, we consider wideband spectrum sensing in the presence of correlation between the occupancies of frequency subbands. We begin by formulating the maximum a posteriori (MAP) estimator of channel occupancy based on measurements from multiple frequency subbands. Since the MAP estimator's complexity grows exponentially with the number of subbands, we propose an alternative structure, in which the subband energy measurements are linearly combined according to a minimum mean-square error (MMSE) criterion to form a sufficient statistic for binary detection in each subband. Through analysis and numerical simulations, we show that the proposed frequency-coupled detector can significantly outperform the traditional decoupled one.